Holomorphic mappings and basic extremal lengths of once-holed tori

被引：3

作者：

Masumoto, Makoto ^{[1
]}

机构：

[1] Yamaguchi Univ, Dept Math, Yamaguchi 7538512, Japan

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 12期

关键词：

Riemann surface; Once-holed torus; Holomorphic mapping; Extremal length; RIEMANN SURFACES; CONFORMAL-MAPPINGS; GENUS ONE;

D O I：

10.1016/j.na.2009.01.136

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are concerned with the set of once-holed tori from which there are handle-preserving holomorphic mappings into a given Riemann surface of positive genus. We investigate how the extremal lengths of homology classes of simple closed curves change under those holomorphic mappings of once-holed tori. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：E1178 / E1181

页数：4

共 10 条

[1] ANALYTIC SELF-MAPPINGS OF RIEMANN SURFACES [J].

MARDEN, A ;

RICHARDS, I ;

RODIN, B .

JOURNAL D ANALYSE MATHEMATIQUE, 1967, 18 :197-&

[2] ON REGIONS BOUNDED BY HOMOTOPIC CURVES [J].

MARDEN, A ;

RICHARDS, I ;

RODIN, B .

PACIFIC JOURNAL OF MATHEMATICS, 1966, 16 (02) :337-&

[3] Holomorphic and conformal mappings of open Riemann surfaces of genus one [J].

Masumoto, M .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 30 (08) :5419-5424

[4] Hyperbolic lengths and conformal embeddings of Riemann surfaces [J].

Masumoto, M .

ISRAEL JOURNAL OF MATHEMATICS, 2000, 116 (1) :77-92

[5] Conformal mappings of a once-holed torus [J].

Masumoto, M .

JOURNAL D ANALYSE MATHEMATIQUE, 1995, 66 :117-136

[6]

MASUMOTO M, 1992, HIROSHIMA MATH J, V22, P573

[7] Once-holed tori embedded in Riemann surfaces [J].

Masumoto, Makoto .

MATHEMATISCHE ZEITSCHRIFT, 2007, 257 (02) :453-464

[8]

SCHIFFER M, 1946, Q J MATH OXFORD SER, V17, P197

[9] THE MODULI OF COMPACT CONTINUATIONS OF AN OPEN RIEMANN SURFACE OF GENUS ONE [J].

SHIBA, M .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 301 (01) :299-311

[10]

SHIBA M, 1984, HIROSHIMA MATH J, V14, P371

← 1 →