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SUMMARY:Hessian operators\, overdetermined problems\, and higher order mea
 n curvatures: symmetry and stability results - Gloria Paoli (Università d
 egli Studi di Napoli Federico II)
DTSTART:20260202T121500Z
DTEND:20260202T124500Z
UID:TALK239857@talks.cam.ac.uk
DESCRIPTION:This is a joint work with Nunzia Gavitone\, Alba Lia Masiello 
 and Giorgio Poggesi.&nbsp\;It is well known that there is a deep connectio
 n between Serrin's symmetry result -- dealing with overdetermined problems
  involving the Laplacian -- and the celebrated Alexandrov's Soap Bubble Th
 eorem (SBT) -- stating that\, if the mean curvature H of the boundary of a
  smooth bounded connected open set&nbsp\; is constant\, then the set&nbsp\
 ; must be a ball.We want to extend the study of such a connection to the b
 roader case of overdetermined problems for Hessian operators and constant 
 higher order mean curvature boundaries. Our analysis will not only provide
  new proofs of the higher order SBT (originally established by Alexandrov)
  and of the symmetry for overdetermined Serrin-type problems for Hessian e
 quations (originally established by Brandolini\, Nitsch\, Salani\, and Tro
 mbetti)\, but also bring several benefits\, including new interesting symm
 etry results and quantitative stability estimates.
LOCATION:Seminar Room 1\, Newton Institute
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