Open Access
February 2019 On positive scalar curvature and moduli of curves
Kefeng Liu, Yunhui Wu
Author Affiliations +
J. Differential Geom. 111(2): 315-338 (February 2019). DOI: 10.4310/jdg/1549422104


In this article we first show that any finite cover of the moduli space of closed Riemann surfaces of genus $g$ with $g \geqslant 2$ does not admit any Riemannian metric $ds^2$ of nonnegative scalar curvature such that ${\lVert \, \cdotp \rVert}_{ds^2} \succ {\lVert \, \cdotp \rVert}_T$ where ${\lVert \, \cdotp \rVert}_T$ is the Teichmüller metric.

Our second result is the proof that any cover $M$ of the moduli space $\mathbb{M}_g$ of a closed Riemann surface $S_g$ does not admit any complete Riemannian metric of uniformly positive scalar curvature in the quasi-isometry class of the Teichmüller metric, which implies a conjecture of Farb–Weinberger in [9].


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Kefeng Liu. Yunhui Wu. "On positive scalar curvature and moduli of curves." J. Differential Geom. 111 (2) 315 - 338, February 2019.


Received: 28 January 2016; Published: February 2019
First available in Project Euclid: 6 February 2019

zbMATH: 07015572
MathSciNet: MR3909910
Digital Object Identifier: 10.4310/jdg/1549422104

Primary: 30F60 , 32G15 , 53C21

Keywords: moduli space , Riemannian metric , Scalar curvature , Teichmüller metric

Rights: Copyright © 2019 Lehigh University

Vol.111 • No. 2 • February 2019
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