| Geometric aspects of the moduli space of Riemann surfaces |
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| 作者姓名： | Shing-Tung Yau |
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| 摘 要： | We describe some recent progress in the study of moduli space of Riemann surfaces in this survey paper. New complete Kahler metrics were introduced on the moduli space and Teichmuller 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 Kahler-Einstein metric. We showed that all the known complete metrics on the moduli space are equivalent and have Poincare type growth. Furthermore, the Kahler-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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Geometric aspects of the moduli space of Riemann surfaces |
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| Shing-Tung Yau.Geometric aspects of the moduli space of Riemann surfaces[J].Science in China(Mathematics),2005,48(Z1). |
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| Authors: | Liu Kefeng SUN Xiaofeng Shing-Tung Yau |
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| Abstract: | We describe some recent progress in the study of moduli space of Riemann surfaces in this survey paper. New complete Kahler metrics were introduced on the moduli space and Teichmuller 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 Kahler-Einstein metric. We showed that all the known complete metrics on the moduli space are equivalent and have Poincare type growth. Furthermore, the Kahler-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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| Keywords: | moduli space Teichmiiller space metric curvature |
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