Existence of good sweepouts on closed manifolds

Lin, Longzhi; Wang, Lu

doi:10.1090/S0002-9939-2010-10451-3

Existence of good sweepouts on closed manifolds
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by Longzhi Lin and Lu Wang PDF

Proc. Amer. Math. Soc. 138 (2010), 4081-4088 Request permission

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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