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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
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Abstract:
In 2007, Z. Huang showed that in the thick part of the moduli space  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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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:
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
Posted:
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 of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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