Convexity of geodesic-length functions: a reprise

Details Convexity of geodesic-length functions: a reprise Convexity of geodesic-length functions: a reprise

2005-02-24

arxiv.org/abs/math/0502526v1

Mathematics

Differential Geometry

14 pages

Scientific paper

New results on the convexity of geodesic-length functions on Teichm\"{u}ller 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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