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
Mathematical Subject Classification 2010
Primary: 53C23
Milestones
Received: 12 March 2014
Revised: 9 September 2014
Accepted: 21 September 2014
Published: 12 April 2015
Authors
Florent Balacheff
Laboratoire Paul Painlevé
Université des Sciences et Technologies
Bâtiment M2
Cité Scientifique
59655 Villeneuve-d’Ascq Cedex
France