Scalar curvature, volume, and Weil-Petersson translation length
Cameron Gates Rudd
Abstract
We construct metrics on pseudoAnosov mapping tori that make every fiber an intrinsically hyperbolic stable minimal surface, and which have scalar curvature identically -6. Using this, we give a new proof (with improved constant) of an inequality bounding the hyperbolic volume of a pseudoAnosov mapping torus by the Weil-Petersson translation length (and consequently, the entropy) of its monodromy.
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