Various domain constants related to uniform perfectness
作者:
Toshiyuki Sugawa,
期刊:
Complex Variables, Theory and Application: An International Journal
(Taylor Available online 1998)
卷期:
Volume 36,
issue 4
页码: 311-345
ISSN:0278-1077
年代: 1998
DOI:10.1080/17476939808815116
出版商: Gordon and Breach Science Publishers
关键词: Uniformly perfect;Schwarzian derivative;extremal length;bounded geometry;1991 Mathematics Subject Classification Primary 30F45;Secondary 30C55;31A15
数据来源: Taylor
摘要:
This is a survey article on domain constants related to uniform perfectness. We gather comparison theorems for various domain constants, most of which are more or less known or elementary but not stated quantitatively in the literature, and some are new or improved results. Among these theorems, our main result is a comparison of the modulus and the injectivity radius of a hyperbolic Riemann surface. Its proof relies upon a comparison of extremal and hyperbolic lengths, which seems to be interesting in itself. And we include a lower estimate of the Hausdorff dimension of a compact set in the Riemann sphere by the modulus of its complement. We also discuss the variance of these domain constants under conformal, quasiconformal or Möbius maps.
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