A local optimal diastolic inequality on the two-sphere

Florent Balacheff (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

Using a ramified cover of the two-sphere by the torus, we prove a local optimal inequality between the diastole and the area on the two-sphere near a singular metric. This singular metric, made of two equilateral triangles glued along their boundary , has been conjectured by E. Calabi to achieve the best ratio area over the square of the length of a shortest closed geodesic. Our diastolic inequality asserts that this conjecture is to some extent locally true.

Mots clés: Conical singularity; diastole; sphere; systole

Domaines: Géométrie différentielle [math.DG]

Florent Balacheff. A local optimal diastolic inequality on the two-sphere. Journal of Topology and Analysis, 2010, 2 (1), pp.109-121. ⟨hal-00336367⟩