Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 973-985

IMPROVED HÖLDER CONTINUITY OF QUASICONFORMAL MAPS

Tyler Bongers

Michigan State University, Department of Mathematics
619 Red Cedar Road, East Lansing, MI 48824, U.S.A.; charlesb 'at' math.msu.edu

Abstract. Quasiconformal maps in the complex plane are homeomorphisms that satisfy certain geometric distortion inequalities; infinitesimally, they map circles to ellipses with bounded eccentricity. The local distortion properties of these maps give rise to a certain degree of global regularity and Hölder continuity. In this paper, we give improved lower bounds for the Hölder continuity of these maps; the analysis is based on combining the isoperimetric inequality with a study of the length of quasicircles. Furthermore, the extremizers for Hölder continuity are characterized, and some applications are given to solutions to elliptic partial differential equations.

2010 Mathematics Subject Classification: Primary 30C62, 26A16.

Key words: Quasiconformal maps, Hölder continuity.

Reference to this article: T. Bongers: Improved Hölder continuity of quasiconformal maps. Ann. Acad. Sci. Fenn. Math. 44 (2019), 973-985.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4465