New results on the geometry of the moduli space of Riemann surfaces

被引：0
|
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] Lehigh University,Department of Mathematics
[4] Harvard University,Department of Mathematics
来源：
Science in China Series A: Mathematics | 2008年 / 51卷
关键词：
moduli spaces; canonical metrics; good metrics; -cohomology; 14D20; 14H20; 32G13; 53C55;
D O I：
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中图分类号：
学科分类号：
摘要：
We briefly survey our recent results about the Mumford goodness of several canonical metrics on the moduli spaces of Riemann surfaces, including the Weil-Petersson metric, the Ricci metric, the Perturbed Ricci metric and the Kahler-Einstein metric. We prove the dual Nakano negativity of the Weil-Petersson metric. As applications of these results we deduce certain important results about the L2-cohomology groups of the logarithmic tangent bundle over the compactified moduli spaces.
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页码：632 / 651
页数：19
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