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arXiv:math/0302242 [math.DG]AbstractReferencesReviewsResources

Mean Curvature Flows and Isotopy of Maps Between Spheres

Mao-Pei Tsui, Mu-Tao Wang

Published 2003-02-19, updated 2011-04-17Version 2

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 homotopic to a constant map.

Comments: 21 pages
Journal: Comm. Pure Appl. Math. 57 (2004), no. 8, 1110-1126
Categories: math.DG, math.AP
Subjects: 53C44
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