Remarks on the variational nature of the heat equation and of mean curvature flow
Giovanni Bellettini and Luca Mugnai
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Submission date: 27. Mar. 2006
MSC-Numbers: 49J45, 53C44, 35K10
Keywords and phrases: heat equation, space-time energy minimizers, mean curvature flow
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We show that the classical solution of the heat equation can be seen as the minimizer of a suitable functional defined in space-time. Using similar ideas, we introduce a functional on the class of space-time tracks of moving hypersurfaces, and we study suitable minimization problems related . We show some connections between minimizers of and mean curvature flow