## Existence of good sweepouts on closed manifolds

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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.## References

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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
- 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
- © Copyright 2010 American Mathematical Society
- 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
- MathSciNet review: 2679629