Teichmüller’s Theorem in Higher Dimensions and Its Applications

Anatoly Golberg, Toshiyuki Sugawa, Matti Vuorinen

研究成果: Article査読

抄録

For a given ring (domain) in R¯ 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 Hölder continuity of quasiconformal mappings of the ball or the half space in Rn.

本文言語English
ページ(範囲)539-558
ページ数20
ジャーナルComputational Methods and Function Theory
20
3-4
DOI
出版ステータスPublished - 2020 11

ASJC Scopus subject areas

  • Analysis
  • Computational Theory and Mathematics
  • Applied Mathematics

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