A1 Refereed original research article in a scientific journal

Teichmüller's Theorem in Higher Dimensions and Its Applications



Authors: Anatoly Golberg, Toshiyuki Sugawa, Matti Vuorinen

Publisher: SPRINGER HEIDELBERG

Publication year: 2020

Journal: Computational Methods and Function Theory

Journal name in source: COMPUTATIONAL METHODS AND FUNCTION THEORY

Journal acronym: COMPUT METH FUNCT TH

Volume: 20

Issue: 3-4

First page : 539

Last page: 558

Number of pages: 20

ISSN: 1617-9447

eISSN: 2195-3724

DOI: https://doi.org/10.1007/s40315-020-00340-x

Self-archived copy’s web address: https://arxiv.org/abs/2006.01565


Abstract
For a given ring (domain) in (R) over bar (n), we discuss whether its boundary components can be separated by an annular ring with modulus nearly equal to that of the given ring. In particular, we show that, for all n >= 3, the standard definition of uniformly perfect sets in terms of the Euclidean metric is equivalent to the boundedness of the moduli of the separating rings. We also establish separation theorems for a "half" of a ring. As applications of those results, we will prove boundary Holder continuity of quasiconformal mappings of the ball or the half space in R-n.

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Last updated on 2024-26-11 at 21:18