The limiting shape of one-dimensional Teichmuller spaces

被引：0

作者：

Sugawa, Toshiyuki ^{[1
]}

机构：

[1] Hiroshima Univ, Grad Sch Sci, Dept Math, Higashihiroshima 7398526, Japan

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 136卷 / 08期

关键词：

cardioid; Teichmuller space; holomorphic motion; once-punctured torus;

D O I：

10.1090/S0002-9939-08-09428-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the Bers embedding of the Teichmuller space of a once-punctured torus converges to the cardioid in the sense of Caratheodory up to rotation when the base torus goes to the boundary of its moduli space.

引用

页码：2849 / 2858

页数：10

共 16 条

[1] RIEMANNS MAPPING THEOREM FOR VARIABLE METRICS [J].

AHLFORS, L ;

BERS, L .

ANNALS OF MATHEMATICS, 1960, 72 (02) :385-404

[2]

BEARDON AF, 1978, J LOND MATH SOC, V18, P475

[3] ON BOUNDARIES OF TEICHMULLER SPACES AND ON KLEINIAN GROUPS .1. [J].

BERS, L .

ANNALS OF MATHEMATICS, 1970, 91 (03) :570-&

[4]

GARDINER FP, 2000, AM MATH SOC PROVIDEN

[5] UNIVERSAL COVERING MAPS FOR VARIABLE REGIONS [J].

HEJHAL, DA .

MATHEMATISCHE ZEITSCHRIFT, 1974, 137 (01) :7-20

[6] REMARKS ON A PAPER BY BERS,L [J].

KALME, CI .

ANNALS OF MATHEMATICS, 1970, 91 (03) :601-&

[7] Drawing Bers embeddings of the Teichmuller space of once-punctured tori [J].

Komori, Y ;

Sugawa, T ;

Wada, M ;

Yamashita, Y .

EXPERIMENTAL MATHEMATICS, 2006, 15 (01) :51-60

[8]

Komori Y., 2004, Conform. Geom. Dyn., V8, P115

[9] Weierstrass points and simple geodesics [J].

McShane, G .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2004, 36 :181-187

[10] The classification of punctured-torus groups [J].

Minsky, YN .

ANNALS OF MATHEMATICS, 1999, 149 (02) :559-626

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