JournalsjemsVol. 10, No. 4pp. 1013–1036

Some aspects of the variational nature of mean curvature flow

  • Giovanni Bellettini

    Università di Roma 'Tor Vergata', Italy
  • Luca Mugnai

    Mathematik in den Naturwissenschaften, Leipzig, Germany
Some aspects of the variational nature of mean curvature flow cover

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 F\mathcal F on the class of space-time tracks of moving hypersurfaces, and we study suitable minimization problems related with F\mathcal F. We show some connections between minimizers of F\mathcal F 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. 1013–1036

DOI 10.4171/JEMS/138