Measurements of Riemannian two-disks and two-spheres

Florent Balacheff (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

We prove that any Riemannian two-sphere with area at most 1 can be continuously mapped onto a tree in a such a way that the topology of fibers is controlled and their length is less than 7.6. This result improves previous estimates and relies on a similar statement for Riemannian two-disks.

Mots clés: closed geodesic; Bers constant; Curvature-free inequalities; isoperimetric inequality; width

Domaines: Géométrie différentielle [math.DG]

Florent Balacheff. Measurements of Riemannian two-disks and two-spheres. Pacific Journal of Mathematics, 2015, 275 (1), pp.167-181. ⟨hal-00937405⟩