Results 51 to 60 of about 5,713 (169)

The boundary distortion of a quasiconformal mapping [PDF]

Pacific Journal of Mathematics, 1994
The authors prove several interesting theorems for quasiconformal maps in \(\mathbb{R}^ n\), \(n\geq 2\). The results are motivated, in part, by Makarov's results for conformal maps. Their first result is: Theorem. Let \(f\) be a \(K\)-quasiconformal mapping of \(B^ n\) into \(\mathbb{R}^ n\).
Heinonen, Juha, Koskela, Pekka
openaire   +2 more sources

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

Harmonic mappings and distance function [PDF]

, 2010
We prove the following theorem: every quasiconformal harmonic mapping between two plane domains with $C^{1,\alpha ...
Kalaj, David
core   +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 means of quasiregular and quasiconformal mappings [PDF]

Proceedings of the American Mathematical Society, 1981
Two theorems are given regarding the means of quasiconformal and quasiregular mappings. Together they show that the principle of subordination for means of analytic functions has no analog, at least in the case of plane quasiregular mappings.
Jerison, David, Weitsman, Allen
openaire   +2 more sources

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

Topological barriers for locally homeomorphic quasiregular mappings in 3-space

, 2017
We construct a new type of locally homeomorphic quasiregular mappings in the 3-sphere and discuss their relation to the M.A.Lavrentiev problem, the Zorich map with an essential singularity at infinity, the Fatou's problem and a quasiregular analogue of ...
Apanasov, Boris N.
core   +1 more source