Convex bodies in Euclidean and Weil-Petersson geometries

Details Convex bodies in Euclidean and Weil-Petersson geometries Convex bodies in Euclidean and Weil-Petersson geometries

2011-10-23

arxiv.org/abs/1110.5022v1

Mathematics

Differential Geometry

Scientific paper

On a convex body in a Euclidean space, we introduce a new variational formulation for its Funk metric, a Finsler metric compatible with the tautological Finsler structure of the convex body. We generalize the metric on Teichmuller spaces with the Weil-Petersson distance function. A set of similarities the resulting metric structure shares with Thurston's asymmetric metric is noted.

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