On Positive Scalar Curvature and Moduli of Curves
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چکیده
In this article we first show that any finite cover of the moduli space of closed Riemann surfaces of genus g with g > 2 does not admit any Riemannian metric ds of nonnegative scalar curvature such that ds dsT where dsT is the Teichmüller metric. Our second result is the proof that any cover M of the moduli space Mg of a closed Riemann surface Sg does not admit any complete Riemannian metric of uniformly positive scalar curvature in the quasiisometry class of the Teichmüller metric, which implies a conjecture of Farb-Weinberger in [Far06].
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تاریخ انتشار 2015