Measurements of Riemannian two-disks and two-spheres

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.

Bibliographic Details
Author: Balacheff, Florent Nicolas|||0000-0001-9770-2954
Format: article
Publication Date:2015
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:287686
Online Access:https://ddd.uab.cat/record/287686
https://dx.doi.org/urn:doi:10.2140/pjm.2015.275.167
Access Level:Open access
Keyword:Bers constant
Closed geodesic
Curvature-free inequalities
Isoperimetric inequalities
Width
Description
Summary: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.