Global and local volume bounds and the shortest geodesic loops
type: Item
instance of: scholarly article
title: Global and local volume bounds and the shortest geodesic loops
zbMATH Open document ID: 1075.53030
author: Stéphane Sabourau
published in: Communications in Analysis and Geometry
publication date: 2005-03-18T00:00:00Z
review text: The author studies relations between the volume of complete Riemannian manifolds and the length of their shortest non trivial geodesic loops under no curvature assumption. By definition, a geodesic loop based at a point * is a geodesic arc with endpoints *. In theorem A the author provides lower bounds on the diameter, on the volume of the whole manifold and on the volume of sufficiently small balls. In theorem B, by introducing the length of geodesic double loops, the author refines the global volume estimate for 2-essential manifolds but the result does not admit any local version.
reviewed by: Rosa Anna Marinosci
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 2147073
MaRDI profile type: Publication
full work available at URL: cag.2004.v12.n5.a3
OpenAlex ID: W2097698452
Wikidata QID: Q125888027
DOI: 10.4310/CAG.2004.V12.N5.A3
description: scientific article; zbMATH DE number 2147073