Mean Curvature Flows and Isotopy of Maps Between Spheres
classification
🧮 math.DG
math.AP
keywords
spherescurvaturedifferentdimensionsmeanpossiblyunitarea-decreasing
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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 homotopic to a constant map.
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