Mean Curvature Flows and Isotopy of Maps Between Spheres

Details Mean Curvature Flows and Isotopy of Maps Between Spheres Mean Curvature Flows and Isotopy of Maps Between Spheres

2003-02-19

arxiv.org/abs/math/0302242v2

Comm. Pure Appl. Math. 57 (2004), no. 8, 1110-1126

Mathematics

Differential Geometry

21 pages

Scientific paper

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.

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