Open Access
January, 2016 Conformal invariants defined by harmonic functions on Riemann surfaces
Hiroshige SHIGA
J. Math. Soc. Japan 68(1): 441-458 (January, 2016). DOI: 10.2969/jmsj/06810441


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.


Download Citation

Hiroshige SHIGA. "Conformal invariants defined by harmonic functions on Riemann surfaces." J. Math. Soc. Japan 68 (1) 441 - 458, January, 2016.


Published: January, 2016
First available in Project Euclid: 25 January 2016

zbMATH: 1336.30062
MathSciNet: MR3454566
Digital Object Identifier: 10.2969/jmsj/06810441

Primary: 32G15
Secondary: 30C40 , 30F60 , 37F30

Keywords: harmonic Hardy space , Harnack distance , hyperbolic distance

Rights: Copyright © 2016 Mathematical Society of Japan

Vol.68 • No. 1 • January, 2016
Back to Top