A note on Riemannian metrics on the moduli space of Riemann surfaces
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- by Yunhui Wu
- Proc. Amer. Math. Soc. 144 (2016), 2513-2519
- DOI: https://doi.org/10.1090/proc/12936
- Published electronically: October 19, 2015
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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.References
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Bibliographic Information
- Yunhui Wu
- Affiliation: Department of Mathematics, Rice University, 6100 Main St, Houston, Texas 77005
- MR Author ID: 866790
- Email: yw22@rice.edu
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2513-2519
- MSC (2010): Primary 30F60, 53C23
- DOI: https://doi.org/10.1090/proc/12936
- MathSciNet review: 3477067