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SUMMARY:The rigidity problem for perimeter inequalities under symmetrizati
 on - Filippo Cagnetti (University of Sussex)
DTSTART:20190527T130000Z
DTEND:20190527T140000Z
UID:TALK122797@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:We will discuss several symmetrization procedures (Steiner\, E
 hrhard\, spherical\, and circular symmetrization) \nthat are known not to 
 increase the perimeter. \nFirst\, we will show how it is possible to chara
 cterize those sets whose perimeter remains unchanged under symmetrization.
  \nAfter that\, we will also characterize rigidity of equality cases. \nBy
  rigidity\, we mean the situation when those sets whose perimeter remains 
 unchanged under symmetrization\, \nare trivially obtained through a rigid 
 motion of the (Steiner\, Ehrhard or spherical) symmetral. \nWe will achiev
 e this through the introduction of a suitable measure-theoretic notion of 
 connectedness\, \nand through a fine analysis of the barycenter function f
 or a special class of sets. \nThese results are obtained together with sev
 eral collaborators \n(Maria Colombo\, Guido De Philippis\, Francesco Maggi
 \, Matteo Perugini\, Dominik Stöger).
LOCATION:MR 13
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