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

DOI:
https://doi.org/10.1090/S0002-9939-2010-10451-3

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 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:
https://doi.org/10.1090/S0002-9939-2010-10451-3

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