Local extremality of the Calabi-Croke sphere for the length of the shortest closed geodesic

Details Local extremality of the Calabi-Croke sphere for the length of the shortest closed geodesic Local extremality of the Calabi-Croke sphere for the length of the shortest closed geodesic

2009-07-13

arxiv.org/abs/0907.2223v1

Mathematics

Differential Geometry

Scientific paper

Recently, F. Balacheff proved that the Calabi-Croke sphere made of two flat 1-unit-side equilateral triangles glued along their boundaries is a local extremum for the length of the shortest closed geodesic among the Riemannian spheres with conical singularities of fixed area. We give an alternative proof of this theorem, which does not make use of the uniformization theorem, and extend the result to Finsler metrics.

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