Conformal invariants defined by harmonic functions on Riemann surfaces

被引：1

作者：

Shiga, Hiroshige ^{[1
]}

机构：

[1] Tokyo Inst Technol, Dept Math, Meguro Ku, Tokyo 1528550, Japan

来源：

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2016年 / 68卷 / 01期

基金：

日本学术振兴会;

关键词：

Harnack distance; harmonic Hardy space; hyperbolic distance;

D O I：

10.2969/jmsj/06810441

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：441 / 458

页数：18

共 50 条

[31] A RUNGE THEOREM FOR HARMONIC-FUNCTIONS ON CLOSED SUBSETS OF RIEMANN SURFACES
BAGBY, T
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 103 (01) : 160 - 164
[32] BANACH SPACES OF BOUNDED DIRICHLET FINITE HARMONIC FUNCTIONS ON RIEMANN SURFACES
Nakai, Mitsuru
[J]. KODAI MATHEMATICAL JOURNAL, 2013, 36 (01) : 15 - 37
[33] SQUARE MEANS VERSUS DIRICHLET INTEGRALS FOR HARMONIC FUNCTIONS ON RIEMANN SURFACES
Masaoka, Hiroaki
Nakai, Mitsuru
[J]. TOHOKU MATHEMATICAL JOURNAL, 2012, 64 (02) : 233 - 259
[34] AUTOMORPHIC-FUNCTIONS, POINCARE-SERIES, AND CONFORMAL FIELDS ON RIEMANN SURFACES
RUHL, W
[J]. FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS, 1988, 36 (12): : 905 - 928
[35] Harmonic surfaces in Riemann metric
Bochner, S.
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1940, 47 (1-3) : 146 - 154
[36] COMPACT RIEMANN SURFACES WITH CONFORMAL INVOLUTIONS
GILMAN, J
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 37 (01) : 105 - 107
[37] HARMONIC APPROXIMATION ON RIEMANN SURFACES
BOIVIN, A
GAUTHIER, PM
[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1984, 36 (01): : 1 - 8
[38] CONFORMAL MAPPING OF OPEN RIEMANN SURFACES
NEHARI, Z
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1950, 68 (MAR) : 258 - 277
[39] CONFORMAL MAPPING OF OPEN RIEMANN SURFACES
NEHARI, Z
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1950, 56 (02) : 168 - 168
[40] Differential Invariants of Conformal and Projective Surfaces
Hubert, Evelyne
Olver, Peter J.
[J]. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2007, 3

← 1 2 3 4 5 →