Results 61 to 70 of about 1,270,291 (205)

First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet

Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1523-1608, September 2025.
Abstract For any p∈(1,∞)$p \in (1,\infty)$, we construct p$p$‐energies and the corresponding p$p$‐energy measures on the Sierpiński carpet. A salient feature of our Sobolev space is the self‐similarity of energy. An important motivation for the construction of self‐similar energy and energy measures is to determine whether or not the Ahlfors regular ...
Mathav Murugan, Ryosuke Shimizu
wiley   +1 more source

On prime end distortion estimates of mappings with the Poletsky condition in domains with the Poincar´e inequality

Математичні Студії
This article is devoted to the study of mappings with bounded and finite distortion defined in some domain of the Euclidean space. We consider mappings that satisfy some upper estimates for the distortion of the modulus of families of paths, where the ...
O. P. Dovhopiatyi, N. S. Ilkevych, E. O. Sevost'yanov, A. L. Targonskii   +3 more
doaj   +1 more source

On the theorem of wan for K-quasiconformal hyperbolic harmonic self mappings of the unit disk [PDF]

Mathematica Moravica, 2015
We give a new glance to the theorem of Wan (Theorem 1.1) which is related to the hyperbolic bi-Lipschicity of the K-quasiconformal, K ≥ 1, hyperbolic harmonic mappings of the unit disk D onto itself.
Knežević Miljan
doaj  

Entire functions with Cantor bouquet Julia sets

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract A hyperbolic transcendental entire function with connected Fatou set is said to be of disjoint type. It is known that the Julia set of a disjoint‐type function of finite order is a Cantor bouquet; in particular, it is a collection of arcs (‘hairs'), each connecting a finite endpoint to infinity.
Leticia Pardo‐Simón, Lasse Rempe
wiley   +1 more source

A Koebe distortion theorem for quasiconformal mappings in the Heisenberg group

Annali di Matematica Pura ed Applicata, 2019
We prove a Koebe distortion theorem for the average derivative of a quasiconformal mapping between domains in the sub-Riemannian Heisenberg group H1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage ...
Tomasz Adamowicz, Katrin Fässler, B. Warhurst   +2 more
semanticscholar   +1 more source

Rigid circle domains with non‐removable boundaries

Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.
Abstract We give a negative answer to the rigidity conjecture of He and Schramm by constructing a rigid circle domain Ω$\Omega$ on the Riemann sphere Ĉ$\hat{\mathbb {C}}$ with conformally non‐removable boundary. Here, rigidity means that every conformal map from Ω$\Omega$ onto another circle domain is a Möbius transformation, and non‐removability ...
Kai Rajala
wiley   +1 more source

On the boundary of an immediate attracting basin of a hyperbolic entire function

Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.
Abstract Let f$f$ be a transcendental entire function of finite order which has an attracting periodic point z0$z_0$ of period at least 2. Suppose that the set of singularities of the inverse of f$f$ is finite and contained in the component U$U$ of the Fatou set that contains z0$z_0$. Under an additional hypothesis, we show that the intersection of ∂U$\
Walter Bergweiler, Jie Ding
wiley   +1 more source

The Theory of Quasiconformal Mappings in Higher Dimensions, I [PDF]

, 2013
We present a survey of the many and various elements of the modern higher-dimensional theory of quasiconformal mappings and their wide and varied application. It is unified (and limited) by the theme of the author's interests.
Gaven J. Martin, Gaven J. Martin
core  

Martin compactifications and quasiconformal mappings [PDF]

Proceedings of the American Mathematical Society, 1985
It is shown that there exists a quasiconformal mapping T T of a Riemann surface R 1 {R_1} onto another R 2 {R_2} such that T T cannot be extended to a homeomorphism of the Martin compactification
Segawa, Shigeo, Tada, Toshimasa
openaire   +1 more source

Lipschitz decompositions of domains with bilaterally flat boundaries

Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.
Abstract We study classes of domains in Rd+1,d⩾2$\mathbb {R}^{d+1},\ d \geqslant 2$ with sufficiently flat boundaries that admit a decomposition or covering of bounded overlap by Lipschitz graph domains with controlled total surface area. This study is motivated by the following result proved by Peter Jones as a piece of his proof of the Analyst's ...
Jared Krandel
wiley   +1 more source