Title	Short geodesic segments on closed Riemannian manifolds
Creator	Rotman, Regina
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2013-08-06
Description	A well-known result of J. P. Serre states that for an arbitrary pair of points on a closed Riemannian manifold there exist infinitely many geodesics connecting these points. A natural question is whether one can estimate the length of the “k-th” geodesic in terms of the diameter of a manifold. We will demonstrate that given any pair of points on a closed Riemannian manifold M of dimension n and diameter d, there always exist at least k geodesics of length at most 4nk2d connecting them. We will also demonstrate that for any two points of a manifold that is diffeomorphic to the 2-sphere, there always exist at least k geodesics between them of length at most 22kd. (Joint with A. Nabutovsky).
Extent	45 minutes
Subject	Mathematics; Differential geometry; Manifolds and cell complexes
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: University of Toronto
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2014-08-06
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivs 2.5 Canada
DOI	10.14288/1.0043484
URI	http://hdl.handle.net/2429/49428
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/2.5/ca/
Aggregated Source Repository	DSpace

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