Calculus of Variations and Geometric Measure Theory

Some results and problems about evolutions of geometric structures

Carlo Mantegazza (Dip. Mat. "Renato Caccioppoli", Univ. Napoli Federico II and Scuola Superiore Meridionale, Napoli)

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".