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

 

Existence of good sweepouts on closed manifolds


Authors: Longzhi Lin and Lu Wang
Journal: Proc. Amer. Math. Soc. 138 (2010), 4081-4088
MSC (2010): Primary 53C22; Secondary 58J35
Published electronically: May 26, 2010
MathSciNet review: 2679629
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Abstract: In this note we establish estimates for the harmonic map heat flow from $ S^1$ into a closed manifold, and we use it to construct sweepouts with the following good property: each curve in the tightened sweepout, whose energy is close to the maximal energy of curves in the sweepout, is itself close to a closed geodesic.


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Additional Information

Longzhi Lin
Affiliation: Department of Mathematics, Johns Hopkins University, 3400 N. Charles Street, Baltimore, Maryland 21218
Email: lzlin@math.jhu.edu

Lu Wang
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
Email: luwang@math.mit.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10451-3
PII: S 0002-9939(2010)10451-3
Received by editor(s): October 8, 2009
Received by editor(s) in revised form: February 4, 2010
Published electronically: May 26, 2010
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2010 American Mathematical Society