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 with . We show some connections between minimizers of and mean curvature flow.
Cite this article
Giovanni Bellettini, Luca Mugnai, Some aspects of the variational nature of mean curvature flow. J. Eur. Math. Soc. 10 (2008), no. 4, pp. 1013–1036DOI 10.4171/JEMS/138