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

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Abstract

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.

Original languageEnglish
Pages (from-to)645-664
Number of pages20
JournalMathematische Zeitschrift
Volume266
Issue number3
DOIs
Publication statusPublished - 2010 Jan 1

Keywords

  • Bergman kernel
  • Petersson series
  • Quadratic differential

ASJC Scopus subject areas

  • Mathematics(all)

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