Calculus of Variations and Geometric Measure Theory

Some results and problems about evolutions of geometric structures

Carlo Mantegazza (Dipartimento di Matematica e Applicazioni "Renato Caccioppoli", Università di Napoli Federico II and Scuola Superiore Meridionale, Napoli, Italy)

created by ambrosio on 13 Jul 2014

17 jul 2014 -- 11:30   [open in google calendar]

Scuola Normale Superiore, Aula Mancini


I will present some results, research lines and open problems about the subject of geometric evolutions, mainly focusing on the two most famous ones: the mean curvature flow of a hypersurface in the Euclidean space and the Ricci flow of a metric on a differential manifold, discussing also some "variations" of the latter, that we recently investigated.

I will discuss some topics that were part of our research in the last years, for instance, the analysis and classification of the self-similar solutions and of their generalizations, and the extensions of these flows to "singular" (non-smooth) objects. Finally, if time allows, I will mention some results about the connections between the two flows, like an unified approach to singularity analysis and the study of their "coupling".