Existence of Good Sweepouts on Closed Manifolds

Details Existence of Good Sweepouts on Closed Manifolds Existence of Good Sweepouts on Closed Manifolds

2009-07-16

arxiv.org/abs/0907.2724v2

Mathematics

Differential Geometry

7 pages; added reference; corrected typos

Scientific paper

In this note we establish estimates for the harmonic map heat flow from $S^1$
into a closed manifold, and 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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