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Homotopy of area decreasing maps by mean curvature flow

Authors:	Andreas Savas-Halilaj Knut Smoczyk

Institution:	1. Institut für Differentialgeometrie, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany;2. Institut für Differentialgeometrie and Riemann Center for Geometry and Physics, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany

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

Keywords:	53C44 53C42 57R52 35K55
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