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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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

Received:
Mar 27, 2006
Published:
Mar 27, 2006
MSC Codes:
49J45, 53C44, 35K10
Keywords:
heat equation, space-time energy minimizers, mean curvature flow

Related publications

Preprint
2006 Repository Open Access
Giovanni Bellettini and Luca Mugnai

Remarks on the variational nature of the heat equation and of mean curvature flow