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MiS Preprint
34/2006
Remarks on the variational nature of the heat equation and of mean curvature flow
Giovanni Bellettini and Luca Mugnai
Abstract
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 $\mathcal{F}$ on the class of space-time tracks of moving hypersurfaces, and we study suitable minimization problems related $\mathcal{F}$. We show some connections between minimizers of $\mathcal{F}$ and mean curvature flow
