# Remarks on the variational nature of heat equation and motion by mean curvature

## Giovanni Bellettini (Dipartimento di Ingegneria dell'Informazione e Scienze Matematiche, Univ. Siena, and International Centre of Theoretical Physics ICTP, Mathematics Section )

created by magnani on 13 Mar 2006
modified on 14 Mar 2006

16 mar 2006

Abstract.

Giovanni Bellettini, from Rome University, "Tor Vergata"

at 18:15 of Thursday 16 March, in Sala dei Seminari'' of the Mathematics Department

will present

Remarks on the variational nature of heat equation and motion by mean curvature.''

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 relate minimizers of $\mathcal F$ to solutions of mean curvature flow.

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