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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Applied Mathematics Seminars: The Rigidity Problem for Symmetrization Inequalities

Presented by Filippo Cagnetti, University of Sussex

17 February 2017 14:00 in CM219

We will discuss several symmetrizations (Steiner, Ehrhard, and spherical symmetrization) that are known not to increase the perimeter. We will show how it is possible to characterize those sets whose perimeter remains unchanged under symmetrization. We will also characterize rigidity of equality cases. By rigidity, we mean the situation when those sets whose perimeter remains unchanged under symmetrization, are trivially obtained through a rigid motion of the (Steiner, Ehrhard or spherical) symmetral. We will achieve this through the introduction of a suitable measure-theoretic notion of connectedness, and through a fine analysis of the barycenter function for a special class of sets. These results are obtained together with several collaborators (Maria Colombo, Guido De Philippis, Francesco Maggi, Matteo Perugini, Dominik Stoger).

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