Mean curvature flows and isotopy of maps between spheres

By Mao-Pei Tsui, Mu-Tao Wang. 2003

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Let f be a smooth map between unit spheres of possibly different dimensions. We prove the global existence and convergence of the mean curvature flow of the graph of f under various conditions. A corollary is that any area‐decreasing map between unit spheres (of possibly different dimensions) is isotopic to a constant map. © 2004 Wiley Periodicals, Inc.

Subfields: Applied Mathematics, Geometry and Topology

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