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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Weil-Petersson geometry of the moduli space of Riemann surfaces
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by Lee-Peng Teo PDF
Proc. Amer. Math. Soc. 137 (2009), 541-552 Request permission

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
  • 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
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 541-552
  • MSC (2000): Primary 30F60, 32G15
  • DOI: https://doi.org/10.1090/S0002-9939-08-09692-5
  • MathSciNet review: 2448574