# Homotopy of area decreasing maps by mean curvature flow

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Let $f:M\to N$ be a smooth area decreasing map between two Riemannian manifolds $(M,\gm)$ and $(N,\gn)$. Under weak and natural assumptions on the curvatures of $(M,\gm)$ and $(N,\gn)$, we prove that the mean curvature flow provides a smooth homotopy of $f$ to a constant map.

Autor: Andreas Savas-Halilaj; Knut Smoczyk

Fuente: https://archive.org/

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