Vol. 275, No. 1, 2015

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Measurements of Riemannian two-disks and two-spheres

Florent Balacheff

Vol. 275 (2015), No. 1, 167–181
Abstract

We prove that any Riemannian two-sphere having area at most $1$ can be continuously mapped onto a tree in such a way that the topology of the 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.

Keywords
Curvature-free inequalities, Bers constant, closed geodesic, isoperimetric inequalities, width
Primary: 53C23