Results for "Olaf Hauk"

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Recurrence required to capture the dynamic computations of the human ventral visual streamMar 14 2019The visual system is an intricate network of brain regions that enables us to recognize the world around us. Despite its abundant lateral and feedback connections, human object processing is commonly viewed and studied as a feedforward process. Here, ... More
First order approach and index theorems for discrete and metric graphsAug 28 2007Sep 03 2007The aim of the present paper is to introduce the notion of first order (supersymmetric) Dirac operators on discrete and metric (``quantum'') graphs. In order to cover all self-adjoint boundary conditions for the associated metric graph Laplacian, we develop ... More
The optimal constants in Khintchine's inequality for the case 2<p<3Jan 28 2016A mean step in Haagerup's proof for the optimal constants in Khintchine's inequality is to show integral inequalities of type $\int(g^s-f^s)\mathrm{d}\mu\geq 0$. F.L. Nazarov and A.N. Podkorytov made Haagerup's proof much more clearer for the case 0<p<2 ... More
On Asteroid EngineeringNov 23 2015I pose the question of maximal Newtonian surface gravity on a homogeneous body of a given mass and volume but with variable shape. In other words, given an amount of malleable material of uniform density, how should one shape it in order for a microscopic ... More
Reconciliation of RDF* and Property GraphsSep 11 2014Nov 13 2014Both the notion of Property Graphs (PG) and the Resource Description Framework (RDF) are commonly used models for representing graph-shaped data. While there exist some system-specific solutions to convert data from one model to the other, these solutions ... More
SPARQL for a Web of Linked Data: Semantics and Computability (Extended Version)Mar 07 2012Apr 06 2012The World Wide Web currently evolves into a Web of Linked Data where content providers publish and link data as they have done with hypertext for the last 20 years. While the declarative query language SPARQL is the de facto for querying a-priory defined ... More
Long baseline experiments with LOFARAug 25 2010I present first results of LOFAR observations with international baselines. An important cornerstone was the detection of the first long-baseline fringes. Their analysis turns out to be extremely useful to investigate and solve a number of technical issues ... More
Why things fallOct 23 2007May 20 2008In this paper we discuss Internal Relativity, a recent program to address the problem of quantum gravity. In our approach we change the relationship between spacetime and matter. Currently we view matter as propagating on spacetime. Einstein's equations ... More
Anomalous elasticity in nematic and smectic elastomer tubuleAug 12 2008We study anomalous elasticity in the tubule phases of nematic and smectic elastomer membranes, which are flat in one direction and crumpled in another. These phases share the same macroscopic symmetry properties including spontaneously-broken in-plane ... More
Early Universe Cosmology in Internal RelativityMay 23 2008We present a new approach to early universe cosmology. Inflation is replaced by a phase transition in which both matter and geometry are created simultaneously. We calculate the spectrum of metric perturbations and show that it is flat. We then argue ... More
Emergent General RelativityApr 18 2006We review different approaches to quantum gravity in which spacetime is emerging. We discuss in some detail the proposals by G. Volovik and S. Lloyd and show how they differ in the way they treat time. We further propose an approach to quantum gravity ... More
On The Origin Of Unidentified EGRET Gamma-Ray SourcesJun 15 2005The identification of celestial gamma-ray sources with astronomical objects or object classes has remained the initial and most fundamental key for understanding their physical nature. The observational characteristic of a gamma-ray emitter and the conditions ... More
Quasilinear Drift Of Cosmic Rays In Weak Turbulent Electromagnetic FieldsJan 13 2005A general quasilinear transport parameter for particle drift in arbitrary turbulence geometry is presented. The new drift coefficient is solely characterized by a nonresonant term and is evaluated for slab and two-dimensional turbulence geometry. The ... More
Quasinormal Modes, the Area Spectrum, and Black Hole EntropyNov 24 2002The results of canonical quantum gravity concerning geometric operators and black hole entropy are beset by an ambiguity labelled by the Immirzi parameter. We use a result from classical gravity concerning the quasinormal mode spectrum of a black hole ... More
From N=2 Fermionic Strings to Superstrings?Dec 31 1994I review the covariant quantization of the critical $N{=}2$ fermionic string with and without a global ${\bf Z}_2$ twist. The BRST analysis yields massless bosonic and fermionic vertex operators in various ghost and picture number sectors, as well as ... More
Continuum estimate of the heavy quark momentum diffusion coefficient $κ$Sep 12 2014Among quantities playing a central role in the theoretical interpretation of heavy ion collision experiments at RHIC and LHC are so-called transport coefficients. Out of those heavy quark diffusion coefficients play an important role e.g. for the analysis ... More
2-universality in randomly perturbed graphsFeb 05 2019A graph $G$ is called universal for a family of graphs $\mathcal{F}$ if it contains every element $F \in \mathcal{F}$ as a subgraph. Let $\mathcal{F}(n,2)$ be the family of all graphs with maximum degree $2$. Ferber, Kronenberg, and Luh [Embedding large ... More
A note on $H^* (\rm{Emb}_0 (M,N))$Jan 25 2002Jan 29 2002Aim of this note is to gain cohomological information about the infinite-dimensional manifold $\rm{Emb}_0 (M,N)$ of asymptotically fixed embeddings of M into N from the topology of the target manifold N. This paper has been withdrawn by the author due ... More
Branched quantum wave guides with Dirichlet boundary conditions: the decoupling caseFeb 03 2005We consider a family of open sets $M_\epsilon$ which shrinks with respect to an appropriate parameter $\epsilon$ to a graph. Under the additional assumption that the vertex neighbourhoods are small we show that the appropriately shifted Dirichlet spectrum ... More
A natural symplectic form for every field theoryAug 21 2001Apr 15 2011The article has been withdrawn as its main result had already been known.
On the von Neumann rule in quantizationMar 25 2019Apr 15 2019We show that any linear quantization map into the space of self-adjoint operators in a Hilbert space violates the von Neumann rule on post-composition with real functions.
A metric approach to Fréchet geometryDec 14 2006Jun 16 2007The aim of this article is to present the category of bounded Frechet manifolds in respect to which we will review the geometry of Frechet manifolds with a stronger accent on its metric aspect. An inverse function theorem in the sense of Nash and Moser ... More
Exact Black-Hole Solution With Self-Interacting Scalar FieldFeb 03 1995Feb 22 1995Einstein gravity minimally coupled to a self-interacting scalar field is investigated in the static and isotropic situation. We explicitly construct in partially closed form a new black-hole solution with exponentially decaying scalar hair. The symmetric ... More
First order operators and boundary triplesNov 14 2007Dec 06 2007The aim of the present paper is to introduce a first order approach to the abstract concept of boundary triples for Laplace operators. Our main application is the Laplace operator on a manifold with boundary; a case in which the ordinary concept of boundary ... More
Consideration of the restriction of lateral contraction in the elastic behaviour of cohesive zone modelsNov 06 2015Cohesive zone models do not consider the lateral contraction of adhesive layers under tensile loads. The constraint of the lateral contraction by the adherents which depends on the geometry of the adhesive layer has a major influence on the normal stiffness ... More
New results on affine invariant pointsSep 20 2015Apr 04 2016We prove a conjecture of B. Gr\"unbaum stating that the set of affine invariant points of a convex body equals to the set of points invariant under all affine linear symmetries of the convex body. As a consequence we give a short proof on the fact that ... More
Internal RelativityMar 12 2012General relativity differs from other forces in nature in that it can be made to disappear locally. This is the essence of the equivalence principle. In general relativity the equivalence principle is implemented using differential geometry. The connection ... More
Time is not the problemApr 22 2009Attempts to quantize general relativity encounter an odd problem. The Hamiltonian that normally generates time evolution vanishes in the case of general relativity as a result of diffeomorphism invariance. The theory seems to be saying that time does ... More
T-duality versus Gauge SymmetryJan 18 2011We review the recently constructed `double field theory' which introduces in addition to the conventional coordinates associated to momentum modes coordinates associated to winding modes. Thereby, T-duality becomes a global symmetry of the theory, which ... More
How light can the lightest neutralino be?Nov 15 2010In this talk we summarize previous work on mass bounds of a light neutralino in the Minimal Supersymmetric Standard Model. We show that without the GUT relation between the gaugino mass parameters M_1 and M_2, the mass of the lightest neutralino is essentially ... More
Dissertation: The Cauchy Problem for MembranesJul 16 2008Aug 10 2008We show existence and uniqueness for timelike minimal submanifolds in ambient Lorentz manifolds admitting a time function. The initial value formulation introduced and the conditions imposed on the initial data are given in purely geometric terms.
Supersymmetric noncommutative solitonsJul 24 2007I consider a supersymmetric Bogomolny-type model in 2+1 dimensions originating from topological string theory. By a gauge fixing this model is reduced to a supersymmetric U(n) chiral model with a Wess-Zumino-Witten-type term in 2+1 dimensions. After a ... More
Smectic elastomer membranesApr 24 2007We present a model for smectic elastomer membranes which includes elastic and liquid crystalline degrees of freedom. Based on our model, we determined the qualitative phase diagram of a smectic elastomer membrane using mean-field theory. This phase diagram ... More
Massive Kaluza-Klein Theories and their Spontaneously Broken SymmetriesDec 21 2006In this thesis we investigate the effective actions for massive Kaluza-Klein states, focusing on the massive modes of spin-3/2 and spin-2 fields. To this end we determine the spontaneously broken gauge symmetries associated to these `higher spin' states ... More
The Cauchy Problem for MembranesJul 22 2008We show existence and uniqueness for timelike minimal submanifolds (world volume of p-branes) in ambient Lorentz manifolds admitting a time function in a neighborhood of the initial submanifold. The initial value formulation introduced and the conditions ... More
WDVV solutions from orthocentric polytopes and Veselov systemsMay 21 2008Jun 26 2008N=4 superconformal n-particle quantum mechanics on the real line is governed by two prepotentials, U and F, which obey a system of partial nonlinear differential equations generalizing the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation. For U=0 one ... More
New Hints from General RelativityJan 10 2004The search for a quantum theory of gravity has followed two parallel but different paths. One aims at arriving at the final theory starting from a priori assumptions as to its form and building it from the ground up. The other tries to infer as much as ... More
LensCLEANing JVAS B0218+357 to determine H0Dec 13 2001We use the radio ring in JVAS B0218+357 to constrain the mass models with LensCLEAN. H0 is determined from the resulting model and the time delay. B0218+357 is one of the best systems to reduce systematic errors in H0 and may thus be called a "golden ... More
Mathematics and Physics of N=2 StringsDec 30 1999Open and closed strings with two worldsheet supersymmetries in 2+2 dimensional spacetime are reviewed in the NSR formulation. I briefly discuss their quantization, mutual and self-interactions, classical spacetime dynamics and interpretation in terms ... More
On the BRST Cohomology of N=2 StringsAug 21 1995We analyze the BRST cohomology of the critical N=2 NSR string using chiral bosonization. Picture-changing and spectral flow is made explicit in a holomorphic field basis. The integration of fermionic and U(1) moduli is performed and yields picture- and ... More
On the von Neumann rule in quantizationMar 25 2019We show that any linear quantization map into the space of self-adjoint operators in a Hilbert space violates the von Neumann rule about post-composition with real functions.
Global Existence and Uniqueness of Minimal Surfaces in Globally Hyperbolic ManifoldsOct 22 2002May 26 2004In this note a proof is given for global existence and uniqueness of minimal surfaces of Lorentzian type from a cylinder into globally hyperbolic Lorentzian manifolds for given initial values up to the first derivatives.
HorizonsNov 19 2011Aug 13 2015We define different notions of black holes, event horizons and Killing horizons for a general time-oriented manifold $(M,g)$ extending previous notions but without the assumption of asymptotical flatness. The notions of 'horizon' are always conformally ... More
On factorizations in perturbative quantum gravityFeb 28 2011Apr 25 2011Some features of Einstein gravity are most easily understood from string theory but are not manifest at the level of the usual Lagrangian formulation. One example is the factorization of gravity amplitudes into gauge theory amplitudes. Based on the recently ... More
SUSY CP phases and asymmetries at collidersApr 21 2009In the Minimal Supersymmetric Standard Model, physical phases of complex parameters lead to CP violation. We show how triple products of particle momenta or spins can be used to construct asymmetries, that allow us to probe these CP phases. To give specific ... More
N=4 Mechanics, WDVV Equations and PolytopesNov 03 2008Nov 17 2008N=4 superconformal n-particle quantum mechanics on the real line is governed by two prepotentials, U and F, which obey a system of partial nonlinear differential equations generalizing the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation for F. The ... More
Gravitational lensingSep 25 2007This is a short and biased review of gravitational lensing with emphasis on the radio and especially VLBI aspects. We briefly explain the basic idea and give a short sketch of the discovery of the first lens, before we more systematically discuss the ... More
Emergent Probabilities in Quantum MechanicsMar 22 2006The transition from the quantum to the classical is governed by randomizing devices (RD), i.e., dynamical systems that are very sensitive to the environment. We show that, in the presence of RDs, the usual arguments based on the linearity of quantum mechanics ... More
Classicality in Quantum MechanicsNov 07 2006In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of classicality ... More
On the infinite-dimensional spin-2 symmetries in Kaluza-Klein theoriesNov 16 2005Jan 25 2006We consider the couplings of an infinite number of spin-2 fields to gravity appearing in Kaluza-Klein theories. They are constructed as the broken phase of a massless theory possessing an infinite-dimensional spin-2 symmetry. Focusing on a circle compactification ... More
Multifractality in a broad class of disordered systemsSep 21 2004We study multifractality in a broad class of disordered systems which includes, e.g., the diluted x-y model. Using renormalized field theory we analyze the scaling behavior of cumulant averaged dynamical variables (in case of the x-y model the angles ... More
Invariants of 3-manifolds from representations of the framed-tangle categoryMar 03 2002A new class of 3-manifold invariants is constructed from representations of the category of framed tangles.
The Gamma-Ray Properties of Unidentified EGRET SourcesFeb 28 2001Although the majority of gamma-ray sources still remain unidentified, we have various kinds of information to characterize the observational properties of unidentified EGRET sources. Despite astronomical properties like locations of individual sources ... More
The Self-Dual Critical N=2 StringJul 13 1996I review the covariant quantization of the closed fermionic string with (2,2) extended world-sheet supersymmetry on R^{2,2}. Results on n-point scattering amplitudes are presented, for tree- and one-loop world-sheets with arbitrary Maxwell instanton number. ... More
Integration Measure and Spectral Flow in the Critical N=2 StringDec 22 1995I present the moduli space of the (2+2)-dimensional critical closed fermionic string with two world-sheet supersymmetries. The integration of fermionic and Maxwell moduli in the presence of punctures yields the string measure for n-point amplitudes at ... More
Semiclassical Approach to Finite-N Matrix ModelsDec 17 1991Dec 18 1991We reformulate the zero-dimensional hermitean one-matrix model as a (nonlocal) collective field theory, for finite~$N$. The Jacobian arising by changing variables from matrix eigenvalues to their density distribution is treated {\it exactly\/}. The semiclassical ... More
A proof of Thorne's Hoop Conjecture for Einstein-Maxwell TheoryJul 18 2016Aug 18 2016We prove different variants of known singularity theorems and finally a statement in the spirit of Thorne's Hoop conjecture, concluding the existence of a region of finite lifetime that includes the outer trapped surface, and of a horizon. Conformal extensions ... More
Beyond information: A bit of meaningNov 06 2013Is our world just information? We argue that our current notion of information has one serious shortcoming: It is quite literally meaningless. We suggest a meaningful extension of the notion of information that is dynamic, internal, approximate, contains ... More
Instantons and Chern-Simons flows in 6, 7 and 8 dimensionsJan 30 2012Feb 23 2012The existence of K-instantons on a cylinder M^7 = R_tau x K/H over a homogeneous nearly K"ahler 6-manifold K/H requires a conformally parallel or a cocalibrated G_2-structure on M^7. The generalized anti-self-duality on M^7 implies a Chern-Simons flow ... More
Metrizability of spaces of homomorphisms between metric vector spacesMay 22 2009Nov 29 2014This note tries to give an answer to the following question: Is there a sufficiently rich class of metric vector spaces such that sufficiently large spaces of continuous linear maps between them are metrizable?
Imaging pulsar echoes at low frequenciesApr 25 2019Interstellar scattering is known to broaden distant objects spatially and temporally. The latter aspect is difficult to analyse, unless the signals carry their own time stamps. Pulsars are so kind to do us this favour. Typically the signature is a broadened ... More
Asymptotic flexibility of globally hyperbolic manifoldsOct 05 2011In this short note, a question of patching together globally hyperbolic manifolds is adressed which appeared in the context of the construction of Hadamard states.
Which spacetimes admit conformal compactifications?Sep 29 2014Nov 21 2014We consider the future causal boundary as a tool to find obstructions to conformal extensions, the latter being a slight generalization to conformal compactifications.
Cheeger-Gromov compactness for manifolds with boundaryAug 20 2018We prove Cheeger-Gromov convergence for a subsequence of a given sequence of manifolds (with boundary) of bounded geometry.
Abstract graph-like space and vector-valued metric graphsMar 30 2016In this note we present some abstract ideas how one can construct spaces from building blocks according to a graph. The coupling is expressed via boundary pairs, and can be applied to very different spaces such as discrete graphs, quantum graphs or graph-like ... More
Spectral analysis of metric graphs and related spacesDec 10 2007Feb 15 2008The aim of the present article is to give an overview of spectral theory on metric graphs guided by spectral geometry on discrete graphs and manifolds. We present the basic concept of metric graphs and natural Laplacians acting on it and explicitly allow ... More
Equilateral quantum graphs and boundary triplesDec 10 2007Jan 15 2008The aim of the present paper is to analyse the spectrum of Laplace and Dirac type operators on metric graphs. In particular, we show for equilateral graphs how the spectrum (up to exceptional eigenvalues) can be described by a natural generalisation of ... More
Probing interstellar scattering towards the Galactic centre with pulsar VLBIJan 19 2015Temporal scatter-broadening can seriously affect our ability to find pulsars orbiting the central mass in our Galaxy. Many of these invaluable probes of geometry around the black hole are expected, but none have been found in close orbits so far, possibly ... More
On the Gribov problem in Yang-Mills theoryDec 21 2013I briefly review the Gribov ambiguity of Yang-Mills theory, some of its features and attempts to control it, in particular the Gribov-Zwanziger proposal to restrict the functional integration in the Landau gauge to the Gribov region. This proposal is ... More
Pulsar scattering in space and timeAug 19 2013We report on a recent global VLBI experiment in which we study the scatter broadening of pulsars in the spatial and time domain simultaneously. Depending on the distribution of scattering screen(s), geometry predicts that the less spatially broadened ... More
The world is discreteJul 23 2013We argue that the scale-free spectrum that is observed in the cosmic microwave background is the result of a phase transition in the early universe. The observed tilt of the spectrum, which has been measured to be 0.04, is shown to be equal to the anomalous ... More
Noncommutative SolitonsOct 10 2007Solitonic objects play a central role in gauge and string theory (as, e.g., monopoles, black holes, D-branes, etc.). Certain string backgrounds produce a noncommutative deformation of the low-energy effective field theory, which allows for new types of ... More
Noncommutative Sine-Gordon ModelSep 09 2004As I briefly review, the sine-Gordon model may be obtained by dimensional and algebraic reduction from 2+2 dimensional self-dual U(2) Yang-Mills through a 2+1 dimensional integrable U(2) sigma model. I argue that the noncommutative (Moyal) deformation ... More
Ln(3) and Black Hole EntropyApr 13 2004Apr 14 2004We review an idea that uses details of the quasinormal mode spectrum of a black hole to obtain the Bekenstein-Hawking entropy of $A/4$ in Loop Quantum Gravity. We further comment on a recent proposal concerning the quasinormal mode spectrum of rotating ... More
Noncommutative Instantons and SolitonsJan 22 2004I explain how to construct noncommutative BPS configurations in four and lower dimensions by solving linear matrix equations. Examples are instantons in D=4 Yang-Mills, monopoles in D=3 Yang-Mills-Higgs, and (moving) solitons in D=2+1 Yang-Mills-Higgs. ... More
A note on $H^1(Emb(M,N))$Feb 06 2002Aim of this note is to extract cohomological information about the manifold $Emb(M,N)$ from the topology of the target manifold N. For special conditions, a monomorphism $H^1 (N) \to H^1 (Emb(M,N))$ is constructed.
Collective Field Theory for D=0 Matrix ModelsDec 14 1993I investigate non-perturbative aspects of zero-dimensional matrix models. Subtleties in the large-$N$ limit of the semiclassical picture are pointed out. The tunneling of eigenvalues is seen to correspond to a chaotic sequence of recursion coefficients ... More
2-universality in randomly perturbed graphsFeb 05 2019Feb 18 2019A graph $G$ is called universal for a family of graphs $\mathcal{F}$ if it contains every element $F \in \mathcal{F}$ as a subgraph. Let $\mathcal{F}(n,2)$ be the family of all graphs with maximum degree $2$. Ferber, Kronenberg, and Luh [Optimal Threshold ... More
Applying the index theorem to non-smooth operatorsJun 15 2015Oct 10 2016We give a simple way to extend index-theoretical statements from partial differential operators with smooth coefficients to operators with coefficients of finite Sobolev order.
Spectral convergence of non-compact quasi-one-dimensional spacesDec 22 2005Jan 02 2006We consider a family of non-compact manifolds $X_\eps$ (``graph-like manifolds'') approaching a metric graph $X_0$ and establish convergence results of the related natural operators, namely the (Neumann) Laplacian $\laplacian {X_\eps}$ and the generalised ... More
Periodic Manifolds with Spectral GapsJul 14 2002We investigate spectral properties of the Laplace operator on a class of non-compact Riemannian manifolds. For a given number $N$ we construct periodic (i.e. covering) manifolds such that the essential spectrum of the corresponding Laplacian has at least ... More
Gate capacitance of back-gated nanowire field-effect transistorsJul 14 2006Gate capacitances of back-gated nanowire field-effect transistors (NW-FETs) are calculated by means of finite element methods and the results are compared with analytical results of the ``metallic cylinder on an infinite metal plate model''. Completely ... More
Gauged diffeomorphisms and hidden symmetries in Kaluza-Klein theoriesNov 30 2006May 11 2007We analyze the symmetries that are realized on the massive Kaluza-Klein modes in generic D-dimensional backgrounds with three non-compact directions. For this we construct the unbroken phase given by the decompactification limit, in which the higher Kaluza-Klein ... More
Noncommutative SolitonsMay 03 2006These lectures deal mainly with solitons in three-dimensional Moyal-deformed sigma models. The topics are: static and moving (multi-)solitons of the (integrable) Ward sigma model, with space-space and time-space noncommutativity, their scattering, moduli ... More
Background Independent Quantum Field Theory and the Cosmological Constant ProblemSep 03 2004Jan 28 2005We introduce the notion of background independent quantum field theory. The distinguishing feature of this theory is that the dynamics can be formulated without recourse to a background metric structure. We show in a simple model how the metric properties ... More
Relational Physics and Quantum SpaceApr 13 2004In a purely relational theory there exists a tension between the relational character of the theory and the existence of quantities like distance and duration. We review this issue in the context of the Leibniz-Clarke correspondence. We then address this ... More
Sagnac effect, twin paradox and space-time topology - Time and length in rotating systems and closed Minkowski space-timesMar 29 2004We discuss the Sagnac effect in standard Minkowski coordinates and with an alternative synchronization convention. We find that both approaches lead to the same result without any contradictions. When applying standard coordinates to the complete rim ... More
Degeneracies and scaling relations in general power-law models for gravitational lensesFeb 20 2002The time delay in gravitational lenses can be used to derive the Hubble constant in a relatively simple way. The results of this method are less dependent on astrophysical assumptions than in many other methods. The most important uncertainty is related ... More
The Perspectives of Democratic Decision-Making in the Information SocietyMay 10 2016In order to structure the debate on the democratic potentials of digital information technology Hubertus Buchstein in 1996 created three ideal types, net optimism, net pessimism and net neutrality. In this study the viability of these positions is put ... More
Not on but ofDec 03 2012In physics we encounter particles in one of two ways. Either as fundamental constituents of the theory or as emergent excitations. These two ways differ by how the particle relates to the background. It either sits on the background, or it is an excitation ... More
Non-linear uplift Ansätze for the internal metric and the four-form field-strength of maximal supergravityFeb 10 2016Jun 15 2016The uplift of SO(8) gauged N=8 supergravity to 11-dimensional supergravity is well studied in the literature. It is given by consistent relations between the respective vector and scalar fields of both theories. For example, recent work provided non-linear ... More
Boundary pairs associated with quadratic formsOct 17 2012May 04 2015We introduce an abstract framework for elliptic boundary value problems in a variational form. Given a non-negative quadratic form in a Hilbert space, a boundary pair consists of a bounded operator, the boundary operator, and an auxiliary Hilbert space, ... More
A note on closed isometric embeddingsMay 30 2008May 20 2016This note is about a little extension of Nash's embedding theorem in the case of complete manifolds.
A note on invariant temporal functionsFeb 09 2015Jul 18 2016The purpose of this article is to present a result on the existence of Cauchy temporal functions invariant by the action of a compact group of conformal transformations in arbitrary globally hyperbolic manifolds. Moreover, the previous results about the ... More
Special temporal functions on globally hyperbolic manifoldsApr 09 2009Oct 22 2012In this article, existence results concerning temporal functions with additional properties on a globally hyperbolic manifold are obtained. These properties are certain bounds on geometric quantities as lapse and shift. The results are linked to completeness ... More
Eigenvalues in Spectral Gaps of a Perturbed Periodic ManifoldJul 14 2002We consider a non-compact Riemannian periodic manifold such that the corresponding Laplacian has a spectral gap. By continuously perturbing the periodic metric locally we can prove the existence of eigenvalues in a gap. A lower bound on the number of ... More
Black holes in Einstein-Maxwell TheoryJul 18 2016Oct 06 2018We prove variants of known singularity theorems ensuring the existence of a region of finite lifetime that are particularly well applicable if the solution admits a conformal extension, a property satisfied e.g. by maximal Cauchy developments of Einstein-Maxwell ... More
Distribution of Transmitted Charge through an Ultrasmall Double-Tunnel JunctionJul 18 1997The transmission of charge through an ultrasmall double junction is considered with Coulomb effects but at zero temperature. We construct an equation which describes the time development of the transmission probability of charges and solve this equation ... More
Weight-conserving characterization of complex functional brain networksMar 26 2011Complex functional brain networks are large networks of brain regions and functional brain connections. Statistical characterizations of these networks aim to quantify global and local properties of brain activity with a small number of network measures. ... More
Convergence of resonances on thin branched quantum wave guidesFeb 21 2007We prove an abstract criterion stating resolvent convergence in the case of operators acting in different Hilbert spaces. This result is then applied to the case of Laplacians on a family $X_\eps$ of branched quantum waveguides. Combining it with an exterior ... More