Results 1 to 10 of about 2,819 (51)

Quasiconformal mappings and minimal Martin boundary of p-sheeted unlimited covering surfaces of the complex plane [PDF]

Kodai Mathematical Journal, 2005
Let \(N(R)\) denote the cardinal number of the minimal Martin boundary of an open Riemann surface \(R\). It was proved by \textit{T. Lyons} [J. Differential Geometry 26, 33--66 (1987; Zbl 0599.60011)] that there exists quasiconformally equivalent open Riemann surfaces \(F_1, F_2\) with \(N(F_1)\neq N(F_2)\).
Masaoka, Hiroaki, Segawa, Shigeo
openaire   +2 more sources

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
core   +1 more source

Loewner theory for quasiconformal extensions: old and new [PDF]

, 2019
This survey article gives an account of quasiconformal extensions of univalent functions with its motivational background from Teichm\"uller theory and classical and modern approaches based on Loewner theory.Comment: 25 pages, 3 figs.
Hotta, Ikkei
core   +3 more sources

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.
core   +1 more source

dbar-equations, integrable deformations of quasiconformal mappings and Whitham hierarchy [PDF]

, 2001
It is shown that the dispersionless scalar integrable hierarchies and, in general, the universal Whitham hierarchy are nothing but classes of integrable deformations of quasiconformal mappings on the plane.
Ahlfors, B. Konopelchenko, Bojarski, Carleson, Dubrovin, Dubrovin, Dubrovin, Gibbons, Iwaniec, Kodama, Kodama, Konopelchenko, Krichever, Krichever, Krichever, Kruskal, L. Martı́nez Alonso, Lawrynowicz, Lax, Lehto, Lehto, Takasaki, Takasaki, Vekua, Wiegmann, Zakharov, Zakharov   +26 more
core   +2 more sources

On injectivity of quasiregular mappings [PDF]

, 2008
We give sufficient conditions for a planar quasiregular mapping to be injective in terms of the range of the differential ...
Iwaniec, Tadeusz, Kovalev, Leonid V., Onninen, Jani   +2 more
core   +3 more sources

On quasiconformal extension of harmonic mappings with nonzero pole

Comptes Rendus. Mathématique
Let $\Sigma _H^k(p)$ be the class of sense-preserving univalent harmonic mappings defined on the open unit disk $\mathbb{D}$ of the complex plane with a simple pole at $z=p \in (0,1)$ that have $k$-quasiconformal extensions ($0\le ...
Bhowmik, Bappaditya, Satpati, Goutam
doaj   +1 more source

Radii of covering disks for locally univalent harmonic mappings

, 2016
For a univalent smooth mapping $f$ of the unit disk $\ID$ of complex plane onto the manifold $f(\ID)$, let $d_f(z_0)$ be the radius of the largest univalent disk on the manifold $f(\ID)$ centered at $f(z_0)$ ($|z_0|
Graf, Sergey Yu., Ponnusamy, Saminathan, Starkov, Victor V.   +2 more
core   +1 more source

On Quasi-inversions [PDF]

, 2015
Given a bounded domain $D \subset {\mathbb R}^n$ strictly starlike with respect to $0 \in D\,,$ we define a quasi-inversion w.r.t. the boundary $\partial D \,.$ We show that the quasi-inversion is bi-Lipschitz w.r.t.
Kalaj, David, Vuorinen, Matti, Wang, Gendi   +2 more
core   +1 more source

Hausdorff dimension of escaping sets of meromorphic functions

, 2020
We give a complete description of the possible Hausdorff dimensions of escaping sets for meromorphic functions with a finite number of singular values. More precisely, for any given $d\in [0,2]$ we show that there exists such a meromorphic function for ...
Aspenberg, Magnus, Cui, Weiwei
core   +2 more sources