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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Spheres of small diameter with long sweep-outs


Author: Yevgeny Liokumovich
Journal: Proc. Amer. Math. Soc. 141 (2013), 309-312
MSC (2010): Primary 53C23
Published electronically: April 20, 2012
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Abstract: We prove the absence of a universal diameter bound on lengths of curves in a sweep-out of a Riemannian 2-sphere. If such a bound existed it would yield a simple proof of the existence of short geodesic segments and closed geodesics on a sphere of small diameter.


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Additional Information

Yevgeny Liokumovich
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada
Email: e.liokumovich@utoronto.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11391-7
PII: S 0002-9939(2012)11391-7
Received by editor(s): June 2, 2011
Published electronically: April 20, 2012
Additional Notes: The author’s research is supported by an NSERC CGS scholarship
Communicated by: Lei Ni
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.