Measurements of Riemannian two-disks and two-spheres

Florent Balacheff

Vol. 275 (2015), No. 1, 167–181

DOI: 10.2140/pjm.2015.275.167

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

Mathematical Subject Classification 2010

Primary: 53C23

Milestones

Received: 12 March 2014

Revised: 9 September 2014

Accepted: 21 September 2014

Published: 12 April 2015