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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

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

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

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

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.

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.

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

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

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

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

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

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

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

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