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Convexity of geodesic-length functions: a reprise

Scott A. Wolpert
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Abstract

New results on the convexity of geodesic-length functions on Teichmüller space are presented. A formula for the Hessian of geodesic-length is presented. New bounds for the gradient and Hessian of geodesic-length are described. A relationship of geodesic-length functions to Weil-Petersson distance is described. Applications to the behavior of Weil-Petersson geodesics are discussed.

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Scott A. Wolpert. 2005-02-24. Convexity of geodesic-length functions: a reprise. https://arxiv.org/abs/math/0502526

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