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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Weil-Petersson geometry of the moduli space of Riemann surfaces


Author: Lee-Peng Teo
Journal: Proc. Amer. Math. Soc. 137 (2009), 541-552
MSC (2000): Primary 30F60, 32G15
Published electronically: September 17, 2008
MathSciNet review: 2448574
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Abstract: In 2007, Z. Huang showed that in the thick part of the moduli space $ \mathcal{M}_g$ of compact Riemann surfaces of genus $ g$, the sectional curvature of the Weil-Petersson metric is bounded below by a constant depending on the injectivity radius, but independent of the genus $ g$. In this article, we prove this result by a different method. We also show that the same result holds for Ricci curvature. For the universal Teichmüller space equipped with a Hilbert structure induced by the Weil-Petersson metric, we prove that its sectional curvature is bounded below by a universal constant.


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Additional Information

Lee-Peng Teo
Affiliation: Faculty of Information Technology, Multimedia University, Jalan Multimedia,Cyberjaya, 63100, Selangor Darul Ehsan, Malaysia
Email: lpteo@mmu.edu.my

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09692-5
PII: S 0002-9939(08)09692-5
Keywords: Moduli space, Riemann surface, Weil--Petersson metric, curvature
Received by editor(s): December 20, 2007
Published electronically: September 17, 2008
Additional Notes: The author would like to thank the Ministry of Science, Technology and Innovation of Malaysia for funding this project under eScienceFund 06-02-01-SF0021.
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.