SOME REMARKS ON THURSTON METRIC AND HYPERBOLIC METRIC

被引：0
|
作者：
Sun, Zongliang [1 ]
机构：
[1] Shenzhen Univ, Dept Math, Shenzhen 518060, Peoples R China
来源：
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2016年 / 53卷 / 02期
关键词：
complex projective structure; hyperbolic metric; marked length spectrum; Teichmuller space; Thurston metric; PROJECTIVE-STRUCTURES; TEICHMULLER SPACE; LENGTH SPECTRUMS; RIEMANN SURFACES; CURVATURE;
D O I：
10.4134/BKMS.2016.53.2.399
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the relations between the Thurston metric and the hyperbolic metric on a closed surface of genus g >= 2. We show a rigidity result which says if there is an inequality between the marked length spectra of these two metrics, then they are isotopic. We obtain some inequalities on length comparisons between these metrics. Besides, we show certain distance distortions under conformal graftings, with respect to the Teichmuller metric, the length spectrum metric and Thurston's asymmetric metrics.
引用
收藏
页码：399 / 410
页数：12
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