Results 41 to 50 of about 1,270,291 (205)

Quasiconformal Mappings and Schwarz's Lemma [PDF]

Transactions of the American Mathematical Society, 1970
In this paper, K quasiconformal maps of Riemann surfaces are investigated. A theorem, which is similar to Schwarz's lemma, is proved for a certain class of K quasiconformal maps. This result is then used to give elementary proofs of theorems concerning K quasiconformal maps.
openaire   +1 more source

On the quasilinear Poisson equations in the complex plane

Доповiдi Нацiональної академiї наук України, 2023
First, we study the existence and regularity of solutions for the linear Poisson equations ∆U(z) = g(z) in bounded domains D of the complex plane £ with charges g in the classes L1(D)∩Llocp(D) , p > 1.
V.Ya. Gutlyanskii, O.V. Nesmelova, V.I. Ryazanov   +2 more
doaj   +1 more source

Modular Equations and Distortion Functions

, 2007
Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings.
B.C. Berndt, B.C. Berndt, C.-Q. He, D. Partyka, D. Partyka, E.T. Whittaker, F. Bowman, G. D. Anderson, G. Martin, G.D. Anderson, G.D. Anderson, G.D. Anderson, G.D. Anderson, G.D. Anderson, J. Hempel, J. Hersch, J. Jenkins, J. Väisälä, J. Väisälä, J. Zaja̧c, J.M. Borwein, M. Vuorinen, M. Vuorinen, M. Vuorinen, M.K. Vamanamurthy, O. Lehto, O. Lehto, P. Seittenranta, P. Tukia, P.F. Byrd, P.P. Belinskii, S. Agard, S. Agard, S. Yamashita, S. Zhang, S.-L. Qiu, S.-L. Qiu, S.-L. Qiu, S.-L. Qiu, S.-L. Qiu, S.-L. Qiu, S.-L. Qiu, S.-L. Qiu, W.K. Hayman, W.K. Hayman, Z. Li   +45 more
core   +2 more sources

Conformality of quasiconformal mappings at a point, revisited [PDF]

Annales Academiae Scientiarum Fennicae: Mathematica, 2018
We present a new and simple proof of Teichm\"uller-Wittich-Belinskii's and Gutlyanskii-Martio's theorems on the conformality of quasiconformal mappings at a given point.
Mitsuhiro Shishikura
semanticscholar   +1 more source

Quasiconformal mappings on the Grushin plane

, 2017
We prove that a self-homeomorphism of the Grushin plane is quasisymmetric if and only if it is metrically quasiconformal and if and only if it is geometrically quasiconformal.
Gartland, Chris, Jung, Derek, Romney, Matthew   +2 more
core   +1 more source

Homogenization of random quasiconformal mappings and random Delauney triangulations [PDF]

Journal of differential geometry, 2019
In this paper, we solve two problems dealing with the homogenization of random media. We show that a random quasiconformal mapping is close to an affine mapping, while a circle packing of a random Delauney triangulation is close to a conformal map ...
Oleg Ivrii, V. Marković
semanticscholar   +1 more source

Lipschitz Continuity of Quasiconformal Mappings and of the Solutions to Second Order Elliptic PDE with Respect to the Distance Ratio Metric [PDF]

, 2017
The main aim of this paper is to study the Lipschitz continuity of certain $$(K, K^{\prime })$$(K,K′)-quasiconformal mappings with respect to the distance ratio metric, and the Lipschitz continuity of the solution of a quasilinear differential equation ...
Peijin Li, S. Ponnusamy
semanticscholar   +1 more source

Dimer models and conformal structures

Communications on Pure and Applied Mathematics, Volume 79, Issue 2, Page 340-446, February 2026.
Abstract Dimer models have been the focus of intense research efforts over the last years. Our paper grew out of an effort to develop new methods to study minimizers or the asymptotic height functions of general dimer models and the geometry of their frozen boundaries.
Kari Astala, Erik Duse, István Prause, Xiao Zhong   +3 more
wiley   +1 more source

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

Beltrami Equations on Rossi Spheres

Mathematics, 2022
Beltrami equations L¯t(g)=μ(·,t)Lt(g) on S3 (where Lt, |t|
Elisabetta Barletta, Sorin Dragomir, Francesco Esposito   +2 more
doaj   +1 more source