A conformally invariant metric on Riemann surfaces associated with integrable holomorphic quadratic differentials

被引：0
作者：
Toshiyuki Sugawa
机构：
[1] Hiroshima University,Department of Mathematics, Graduate School of Science
[2] Tohoku University,Graduate School of Information Sciences
来源：
Mathematische Zeitschrift | 2010年 / 266卷
关键词：
Quadratic differential; Petersson series; Bergman kernel; Primary 30F45; Secondary 30C40;
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摘要：
In this paper, we define a conformally invariant (pseudo-)metric on all Riemann surfaces in terms of integrable holomorphic quadratic differentials and analyze it. This metric is closely related to an extremal problem on the surface. As a result, we have a kind of reproducing formula for integrable quadratic differentials. Furthermore, we establish a new characterization of uniform thickness of hyperbolic Riemann surfaces in terms of invariant metrics.
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页码：645 / 664
页数：19
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  • [11] Pommerenke C.(2001)An explicit bound for uniform perfectness of Julia sets of rational maps Math. Z. 238 317-333
  • [12] Suita N.(2001)Uniform perfectness of the limit sets of Kleinian groups Trans. Am. Math. Soc. 353 3603-3615
  • [13] Sugawa T.(1992)Spectral limits for hyperbolic surfaces, II Invent. Math. 108 91-129
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