Results 1 to 10 of about 450 (47)
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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An N-dimensional version of the Beurling-Ahlfors extension [PDF]
, 2009 We extend monotone quasiconformal mappings from dimension n to n+1 while preserving both monotonicity and quasiconformality. The extension is given explicitly by an integral operator.
Kovalev, Leonid V., Onninen, Jani
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On quasiplanes in Euclidean spaces [PDF]
, 2007 A variational inequality for the images of $k$-dimensional hyperplanes under quasiconformal maps of the $n$-dimensional Euclidean space is proved when $1\le k\le n-2 .$Comment: 12 ...
Martio, Olli +2 more
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Chordal Hausdorff Convergence and Quasihyperbolic Distance
Analysis and Geometry in Metric Spaces, 2020 We study Hausdorff convergence (and related topics) in the chordalization of a metric space to better understand pointed Gromov-Hausdorff convergence of quasihyperbolic distances (and other conformal distances).
Herron David A. +2 more
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Hausdorff measure of the singular set of quasiregular maps on Carnot groups
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 35, Page 2203-2220, 2003., 2003 Recently, the theory of quasiregular mappings on Carnot groups has been developed intensively. Let ν stand for the homogeneous dimension of a Carnot group and let m be the index of the last vector space of the corresponding Lie algebra. We prove that the (ν − m − 1)‐dimensional Hausdorff measure of the image of the branch set of a quasiregular mapping ...
Irina Markina
wiley +1 more source
The Apollonian metric: limits of the comparison and bilipschitz properties
Abstract and Applied Analysis, Volume 2003, Issue 20, Page 1141-1158, 2003., 2003 The Apollonian metric is a generalization of the hyperbolic metric. It is defined in arbitrary domains in ℝn. In this paper, we derive optimal comparison results between this metric and the jG metric in a large class of domains. These results allow us to prove that Euclidean bilipschitz mappings have small Apollonian bilipschitz constants in a domain G
Peter A. Hästö
wiley +1 more source
Ar (λ)‐weighted Caccioppoli‐type and Poincaré‐type inequalities for A‐harmonic tensors
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 2, Page 115-122, 2002., 2002 We prove a local version of weighted Caccioppoli‐type inequality, then we prove a version of weighted Poincaré‐type inequality for A‐harmonic tensors both locally and globally. Ar(λ)-weighted Caccioppoli-type and Poincaré-type inequalities for A-harmonic tensors (erratum)dx.doi.org/10.1155 ...
Bing Liu
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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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Quasiregular mappings of polynomial type in R^2 [PDF]
, 2010 Complex dynamics deals with the iteration of holomorphic functions. As is well- known, the first functions to be studied which gave non-trivial dynamics were quadratic polynomials, which produced beautiful computer generated pictures of Julia sets and ...
Fletcher, Alastair, Goodman, Dan
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Close-to-convexity of quasihyperbolic and $j$-metric balls
, 2010 We will consider close-to-convexity of the metric balls defined by the quasihyperbolic metric and the $j$-metric. We will show that the $j$-metric balls with small radii are close-to-convex in general subdomains of $\Rn$ and the quasihyperbolic balls ...
Klén, Riku
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