Geometric aspects of the moduli space of riemann surfaces

被引：7
作者：
Kefeng Liu
Xiaofeng Sun
Shing-Tung Yau
机构：
[1] Zhejiang University,Center of Mathematical Sciences
[2] University of California at Los Angeles,Department of Mathematics
[3] Harvard University,Department of Mathematics
来源：
Science in China Series A: Mathematics | 2005年 / 48卷
关键词：
moduli space; Teichmüller space; metric; curvature;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We describe some recent progress in the study of moduli space of Riemann surfaces in this survey paper. New complete Kähler metrics were introduced on the moduli space and Teichmüller space. Their curvature properties and asymptotic behavior were studied in details. These natural metrics served as bridges to connect all the known canonical metrics, especially the Kähler-Einstein metric. We showed that all the known complete metrics on the moduli space are equivalent and have Poincaré type growth. Furthermore, the Kähler-Einstein metric has strongly bounded geometry. This also implied that the logarithm cotangent bundle of the moduli space is stable in the sense of Mumford.
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页码：97 / 122
页数：25
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