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Short geodesic segments on closed Riemannian manifolds Rotman, Regina 2013-08-06
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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 |
FileFormat | 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/ |
AggregatedSourceRepository | DSpace |
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https://iiif.library.ubc.ca/presentation/dsp.48630.1-0043484/manifest