Results 1 to 10 of about 2,942 (81)

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   +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   +3 more sources

Distortion of area and dimension under quasiconformal mappings in the plane. [PDF]

Proc Natl Acad Sci U S A, 1993
Astala K.
europepmc   +2 more sources

Triangular Ratio Metric Under Quasiconformal Mappings in Sector Domains [PDF]

Computational methods in Function Theory, 2020
The hyperbolic metric and different hyperbolic type metrics are studied in open sector domains of the complex plane. Several sharp inequalities are proven for them.
O. Rainio, M. Vuorinen
semanticscholar   +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

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

Criteria for univalence and quasiconformal extension of harmonic mappings in terms of the Schwarzian derivative [PDF]

Archiv der Mathematik, 2014
We prove that if the Schwarzian norm of a given complex-valued locally univalent harmonic mapping f in the unit disk is small enough, then f is, indeed, globally univalent in the unit disk and can be extended to a quasiconformal mapping in the extended ...
R. Hernández, María J. Martín
semanticscholar   +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

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

Nonlinear Dynamics on the Plane and Integrable Hierarchies of Infinitesimal Deformations [PDF]

, 2002
A class of nonlinear problems on the plane, described by nonlinear inhomogeneous $\bar{\partial}$-equations, is considered. It is shown that the corresponding dynamics, generated by deformations of inhomogeneous terms (sources) is described by Hamilton ...
Alonso, L. Martinez, Konopelchenko, B.
core   +3 more sources