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SUMMARY:The rigidity problem for perimeter inequalities under symmetrizati
 on - Filippo Cagnetti (University of Sussex)
DTSTART:20190527T130000Z
DTEND:20190527T140000Z
UID:TALK125269@talks.cam.ac.uk
CONTACT:Ivan Moyano
DESCRIPTION:We will discuss several symmetrization procedures (Steiner\, E
 hrhard\, spherical\, and circular symmetrization) that are known not to in
 crease the perimeter. First\, we will show how it is possible to character
 ize those sets whose perimeter remains unchanged under symmetrization. Aft
 er that\, we will also characterize rigidity of equality cases. By rigidit
 y\, we mean the situation when those sets whose perimeter remains unchange
 d under symmetrization\, are trivially obtained through a rigid motion of 
 the (Steiner\, Ehrhard or spherical) symmetral. We will achieve this throu
 gh the introduction of a suitable measure-theoretic notion of connectednes
 s\, and through a fine analysis of the barycenter function for a special c
 lass of sets. These results are obtained together with several collaborato
 rs (Maria Colombo\, Guido De Philippis\, Francesco Maggi\, Matteo Perugini
 \, Dominik Stöger).
LOCATION:CMS\, MR13
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