Existence of good sweepouts on closed manifolds
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Existence of good sweepouts on closed manifolds

  • Author(s): Lin, Longzhi
  • Wang, Lu
  • et al.
Abstract

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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