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

Author(s): Lee-Peng Teo
Journal: Proc. Amer. Math. Soc. 137 (2009), 541-552.
MSC (2000): Primary 30F60, 32G15
Posted: September 17, 2008
MathSciNet review: 2448574
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Abstract | References | Similar articles | Additional information

Abstract: In 2007, Z. Huang showed that in the thick part of the moduli space $\mathcal{M}_g$ of compact Riemann surfaces of genus , the sectional curvature of the Weil-Petersson metric is bounded below by a constant depending on the injectivity radius, but independent of the genus . 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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