Results 1 to 10 of about 133 (28)
Analysis and Geometry in Metric Spaces, 2021 We extend the classical Carathéodory extension theorem to quasiconformal Jordan domains (Y, dY). We say that a metric space (Y, dY) is a quasiconformal Jordan domain if the completion ̄Y of (Y, dY) has finite Hausdorff 2-measure, the boundary ∂Y = ̄Y \ Y
Ikonen Toni
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Conformal Transformation of Uniform Domains Under Weights That Depend on Distance to The Boundary
Analysis and Geometry in Metric Spaces, 2022 The sphericalization procedure converts a Euclidean space into a compact sphere. In this note we propose a variant of this procedure for locally compact, rectifiably path-connected, non-complete, unbounded metric spaces by using conformal deformations ...
Gibara Ryan, Shanmugalingam Nageswari
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Quasisymmetric Koebe uniformization with weak metric doubling measures
, 2021 We give a characterization of metric spaces quasisymmetrically equivalent to a finitely connected circle domain.
Rajala, Kai, Rasimus, Martti
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Duality of Moduli and Quasiconformal Mappings in Metric Spaces
Analysis and Geometry in Metric Spaces, 2020 We prove a duality relation for the moduli of the family of curves connecting two sets and the family of surfaces separating the sets, in the setting of a complete metric space equipped with a doubling measure and supporting a Poincaré inequality.
Jones Rebekah, Lahti Panu
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An Approach to Studying Quasiconformal Mappings on Generalized Grushin Planes [PDF]
, 2014 We demonstrate that the complex plane and a class of generalized Grushin planes $G_r$, where $r$ is a function satisfying specific requirements, are quasisymmetrically equivalent.
Ackermann, Colleen
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Topological Conformal Dimension [PDF]
, 2015 We investigate a quasisymmetrically invariant counterpart of the topological Hausdorff dimension of a metric space. This invariant, called the topological conformal dimension, gives a lower bound on the topological Hausdorff dimension of quasisymmetric ...
DiMarco, Claudio A.
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Pull-Back of Metric Currents and Homological Boundedness of BLD-Elliptic Spaces
Analysis and Geometry in Metric Spaces, 2019 Using the duality of metric currents and polylipschitz forms, we show that a BLD-mapping f : X → Y between oriented cohomology manifolds X and Y induces a pull-back operator f* : Mk,loc(Y) → Mk,loc(X) between the spaces of metric k-currents of locally ...
Pankka Pekka, Soultanis Elefterios
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Modulus of surface families and the radial stretch in the Heisenberg group [PDF]
, 2015 We develop a modulus method for surface families inside a domain in the Heisenberg group and we prove that the stretch map between two Heisenberg spherical rings is a minimiser for the mean distortion among the class of contact quasiconformal maps ...
Platis, Ioannis D.
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On derivations of subalgebras of real semisimple Lie algebras [PDF]
, 2018 Let g be a real semisimple Lie algebra with Iwasawa decomposition k+a+n. We show that, except for some explicit exceptional cases, every derivation of the nilpotent subalgebra n that preserves its restricted root space decomposition is of the form ad( W),
Ciatti, Paolo, Cowling,, Michael, G.
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A Newman property for BLD-mappings
, 2019 We define a Newman property for BLD-mappings and study its connections to the porosity of the branch set in the setting of generalized manifolds equipped with complete path ...
Luisto, Rami
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