Resumen de Existence of good sweepouts on closed manifolds

Longzhi Lin, Lu Wang

• 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.