Conformal invariants defined by harmonic functions on Riemann surfaces

• Shiga Hiroshige

  Department of Mathematics, Tokyo Institute of Technology

Abstract

In this paper, we consider conformal invariants defined by various spaces of harmonic functions on Riemann surfaces. The Harnack distance is a typical one. We give sharp inequalities comparing those invariants with the hyperbolic metric on the Riemann surface and we determine when equalities hold. We also describe the Harnack distance in terms of the Martin compactification and discuss some properties of the distance.

Journal

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 68 (1), 441-458, 2016

  The Mathematical Society of Japan

Keywords

• Harnack distance
• harmonic Hardy space
• hyperbolic distance

Details

• CRID: 1390282680092489600
• NII Article ID: 130005122700
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/06810441
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL BIB ID: 027060945
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I027060945
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed