Some aspects of the variational nature of mean curvature flow

• Autores: Giovanni Bellettini, Luca Mugnai
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 10, Nº 4, 2008, págs. 1013-1036
• Idioma: inglés
• DOI: 10.4171/jems/138
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• Resumen

  • 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 with $\mathcal F$. We show some connections between minimizers of $\mathcal F$ and mean curvature flow