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A note on Riemannian metrics on the moduli space of Riemann surfaces


Author: Yunhui Wu
Journal: Proc. Amer. Math. Soc. 144 (2016), 2513-2519
MSC (2010): Primary 30F60, 53C23
DOI: https://doi.org/10.1090/proc/12936
Published electronically: October 19, 2015
MathSciNet review: 3477067
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Abstract: In this note we show that the moduli space $ \mathbb{M}(S_{g,n})$ of surface $ S_{g,n}$ of genus $ g$ with $ n$ punctures, satisfying $ 3g+n\geq 5$, admits no complete Riemannian metric of nonpositive sectional curvature such that the Teichmüller space $ \mathbb{T}(S_{g,n})$ is a mapping class group $ \mathrm {Mod}(S_{g,n})$-invariant visibility manifold.


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Additional Information

Yunhui Wu
Affiliation: Department of Mathematics, Rice University, 6100 Main St, Houston, Texas 77005
Email: yw22@rice.edu

DOI: https://doi.org/10.1090/proc/12936
Keywords: Moduli space, visibility manifold, Riemannian metric
Received by editor(s): June 26, 2015
Received by editor(s) in revised form: July 9, 2015
Published electronically: October 19, 2015
Communicated by: Michael Wolf
Article copyright: © Copyright 2015 American Mathematical Society