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Article

Asymptotic Conformality and Polygonal Approximation

by
Samuel L. Krushkal
1,2
1
Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel
2
Department of Mathematics, University of Virginia, Charlottesville, VA 22904-4137, USA
Axioms 2024, 13(6), 376; https://doi.org/10.3390/axioms13060376
Submission received: 20 March 2024 / Revised: 22 May 2024 / Accepted: 31 May 2024 / Published: 3 June 2024
(This article belongs to the Special Issue Advanced Approximation Techniques and Their Applications, 2nd Edition)

Abstract

Univalent functions with asymptotically conformal extension to the boundary form a subclass of functions with quasiconformal extension with rather special features. Such functions arise in various questions of geometric function theory and Teichmüller space theory and have important applications involving conformal and quasiconformal maps. The paper provides an approximative characterization of local conformality and its connection with univalent polynomials. Also, some other quantitative applications of this connection are given.
Keywords: univalent function; quasiconformal extensions and reflections; Grunsky and Teichmüller norms; universal Teichmüller space; hyperbolic metric; generalized Gaussian curvature; Minda’s maximum principle; holomorphic quadratic differentials; Fredholm eigenvalues univalent function; quasiconformal extensions and reflections; Grunsky and Teichmüller norms; universal Teichmüller space; hyperbolic metric; generalized Gaussian curvature; Minda’s maximum principle; holomorphic quadratic differentials; Fredholm eigenvalues

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MDPI and ACS Style

Krushkal, S.L. Asymptotic Conformality and Polygonal Approximation. Axioms 2024, 13, 376. https://doi.org/10.3390/axioms13060376

AMA Style

Krushkal SL. Asymptotic Conformality and Polygonal Approximation. Axioms. 2024; 13(6):376. https://doi.org/10.3390/axioms13060376

Chicago/Turabian Style

Krushkal, Samuel L. 2024. "Asymptotic Conformality and Polygonal Approximation" Axioms 13, no. 6: 376. https://doi.org/10.3390/axioms13060376

APA Style

Krushkal, S. L. (2024). Asymptotic Conformality and Polygonal Approximation. Axioms, 13(6), 376. https://doi.org/10.3390/axioms13060376

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