Journal of the Mathematical Society of Japan

Conformal invariants defined by harmonic functions on Riemann surfaces

Hiroshige SHIGA

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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.

Article information

Source
J. Math. Soc. Japan, Volume 68, Number 1 (2016), 441-458.

Dates
First available in Project Euclid: 25 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1453731548

Digital Object Identifier
doi:10.2969/jmsj/06810441

Mathematical Reviews number (MathSciNet)
MR3454566

Zentralblatt MATH identifier
1336.30062

Subjects
Primary: 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]
Secondary: 30C40: Kernel functions and applications 30F60: Teichmüller theory [See also 32G15] 37F30: Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems

Keywords
Harnack distance harmonic Hardy space hyperbolic distance

Citation

SHIGA, Hiroshige. Conformal invariants defined by harmonic functions on Riemann surfaces. J. Math. Soc. Japan 68 (2016), no. 1, 441--458. doi:10.2969/jmsj/06810441. https://projecteuclid.org/euclid.jmsj/1453731548


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References

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