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Surface subgroups on 1-vertex and 3-vertex polyhedra forming triangular hyperbolic buildingsOct 17 2014Jul 17 2015In this article we study surface subgroups of groups acting simply transitively on vertex sets of certain hyperbolic triangular buildings. Kangaslampi and Vdovina have constructed and classified all groups acting simply transitively on the vertices of ... More

Triangular hyperbolic buildingsJun 30 2005We construct triangular hyperbolic polyhedra whose links are generalized 4-gons. The universal cover of those polyhedra are hyperbolic buildings, which appartments are hyperbolic planes tesselated by regular triangles with angles $\pi/4$. Moreover, the ... More

Hyperbolic triangular buildings without periodic planes of genus twoSep 04 2014Oct 19 2015We study surface subgroups of groups acting simply transitively on vertex sets of certain hyperbolic triangular buildings. The study is motivated by Gromov's famous surface subgroup question: Does every one-ended hyperbolic group contain a subgroup which ... More

Groups acting simply transitively on hyperbolic buildingsJul 19 2011Oct 31 2011We construct and classify all groups, given by triangular presentations associated to the smallest thick generalized quadrangle, that act simply transitively on the vertices of hyperbolic triangular buildings of the smallest non-trivial thickness. Our ... More

Spectra of linear fractional composition operators on the Hardy and weighted Bergman spaces of the half-planeMay 06 2016Nov 24 2016We compute the spectra and the essential spectra of bounded linear fractional composition operators acting on the Hardy and weighted Bergman spaces of the upper half-plane. We are also able to extend the results to weighted Dirichlet spaces of the upper ... More

Erratum for Ricci-flat graphs with girth at least fiveFeb 08 2018This erratum will correct the classification of Theorem 1 in Lin-Lu-Yau, Comm. Anal. Geom., 2014, that misses the Triplex graph.

Ricci-flat cubic graphs with girth fiveFeb 08 2018We classify all connected, simple, 3-regular graphs with girth at least 5 that are Ricci-flat. We use the definition of Ricci curvature on graphs given in Lin-Lu-Yau, Tohoku Math., 2011, which is a variation of Ollivier, J. Funct. Anal., 2009. A graph ... More

Erratum for Ricci-flat graphs with girth at least fiveFeb 08 2018May 08 2019This erratum will correct the classification of Theorem 1 in Lin-Lu-Yau, Comm. Anal. Geom., 2014, that misses the Triplex graph.

Equivalence and self-improvement of p-fatness and Hardy's inequality, and association with uniform perfectnessSep 13 2007Jan 14 2008We present an easy proof that $p$--Hardy's inequality implies uniform $p$--fatness of the boundary when $p=n$. The proof works also in metric space setting and demonstrates the self--improving phenomenon of the $p$--fatness. We also explore the relationship ... More

Smoothness spaces of higher order on lower dimensional subsets of the Euclidean spaceSep 09 2011We study Sobolev type spaces defined in terms of sharp maximal functions on Ahlfors regular subsets of the Euclidean space and the relation between these spaces and traces of classical Sobolev spaces.

Measure of curves in graded groupsSep 27 2010We establish an area-type formula for the intrinsic spherical Hausdorff measure of every regular curve embedded in an arbitrary graded group.

Characterizations of Sobolev inequalities on metric spacesSep 07 2007Jan 14 2008We present isocapacitary characterizations of Sobolev inequalities in very general metric measure spaces.

Lower semicontinuous obstacles for the porous medium equationJul 20 2018We deal with the obstacle problem for the porous medium equation in the slow diffusion regime $m>1$. Our main interest is to treat fairly irregular obstacles assuming only boundedness and lower semicontinuity. In particular, the considered obstacles are ... More

Strong A-infinity weights are A-infinity weights on metric spacesAug 11 2009We prove that every strong A-infinity weight is a Muckenhoupt weight in Ahlfors-regular metric measure spaces that support a Poincare inequality. We also explore the relations between various definitions for A-infinity weights in this setting, since some ... More

The equivalence between pointwise Hardy inequalities and uniform fatnessJun 11 2009We prove an equivalence result between the validity of a pointwise Hardy inequality in a domain and uniform capacity density of the complement. This result is new even in Euclidean spaces, but our methods apply in general metric spaces as well. We also ... More

Minima of quasisuperminimizersMay 19 2015Let u_i be a Q_i-quasisuperminimizer, i=1,2, and u=min{u_1,u_2}, where 1 <= Q_1 <= Q_2. Then u is a quasisuperminimizer, and we improve upon the known upper bound (due to Kinnunen and Martio) for the optimal quasisuperminimizing constant Q of u. We give ... More

Homeomorphisms of the Heisenberg group preserving BMOSep 30 2015We provide a new geometric proof of Reimann's theorem characterizing quasiconformal mappings as the ones preserving functions of bounded mean oscillation. While our proof is new already in the Euclidean spaces, it is applicable in Heisenberg groups as ... More

Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a $1$-Poincaré inequalitySep 11 2018We consider two notions of functions of bounded variation in complete metric measure spaces, one due to Martio and the other due to Miranda~Jr. We show that these two notions coincide, if the measure is doubling and supports a $1$-Poincar\'e inequality. ... More

Stability and continuity of functions of least gradientOct 08 2014Oct 09 2014In this note we prove that on metric measure spaces, functions of least gradient, as well as local minimizers of the area functional (after modification on a set of measure zero) are continuous everywhere outside their jump sets. As a tool, we develop ... More

A maximal function approach to two-measure Poincaré inequalitiesJan 22 2018This paper extends the self-improvement result of Keith and Zhong in [16] to the two-measure case. Our main result shows that a two-measure $(p,p)$-Poincar\'e inequality for $1<p<\infty$ improves to a $(p,p-\varepsilon)$-Poincar\'e inequality for some ... More

Transparent pronunciation scoring using articulatorily weighted phoneme edit distanceMay 07 2019For researching effects of gamification in foreign language learning for children in the "Say It Again, Kid!" project we developed a feedback paradigm that can drive gameplay in pronunciation learning games. We describe our scoring system based on the ... More

The space $JN_p$: nontriviality and dualityApr 21 2017Feb 01 2018We study a function space $JN_p$ based on a condition introduced by John and Nirenberg as a variant of BMO. It is known that $L^p\subset JN_{p}\subsetneq L^{p,\infty}$, but otherwise the structure of $JN_p$ is largely a mystery. Our first main result ... More

A characterization of BMO self-maps of a metric measure spaceAug 19 2013Oct 01 2015This paper studies functions of bounded mean oscillation (BMO) on metric spaces equipped with a doubling measure. The main result gives characterizations for mappings that preserve BMO. This extends the corresponding Euclidean results by Gotoh to metric ... More

On Whitney-type characterization of approximate differentiability on metric measure spacesJul 25 2012We study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is a Whitney-type characterization of approximately differentiable functions in this setting. As an application, we ... More

Regularity of sets with quasiminimal boundary surfaces in metric spacesMay 16 2011This paper studies regularity of perimiter quasiminimizing sets in metric measure spaces with a doubling measure and a Poincare inequality. The main result shows that the measure theoretic boundary of a quasiminimizing set coincides with the topological ... More

Spin dependent electron transport through a magnetic resonant tunneling diodeNov 24 2004Electron transport properties in nanostructures can be modeled, for example, by using the semiclassical Wigner formalism or the quantum mechanical Green's functions formalism. We compare the performance and the results of these methods in the case of ... More

Dynamic MRI Reconstruction from Undersampled Data with an Anatomical PrescanNov 30 2017The goal of dynamic magnetic resonance imaging (dynamic MRI) is to visualize tissue properties and their local changes over time that are traceable in the MR signal. We propose a new variational approach for the reconstruction of subsampled dynamic MR ... More