Care tutte, cari tutti, giovedì 11 gennaio alle ore 17:00, in Sala Riunioni, per il seminario di Analisi Matematica, avremo il piacere di ascoltare Rossano Sannipoli (Dipartimento di Matematica, Università di Pisa), che terrà un seminario dal titolo “Some isoperimetric inequality involving the boundary momentum and curvature integrals”. Trovate qui sotto l’abstract. Il seminario sarà preceduto da una merenda nella sala caffè del piano terra, dalle ore 16:30.
A presto, Ilaria Lucardesi e Luigi Forcella
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Dear all, On Thursday 11th at 5:00 PM, in "Sala Riunioni", for the Mathematical Analysis Seminar, we will have the pleasure of listening to Rossano Sannipoli (Math Department, University of Pisa). The title of the talk is “Some isoperimetric inequality involving the boundary momentum and curvature integrals”. Please find below the abstract. The seminar will be preceded by a snack in the coffee room on the ground floor, starting at 4:30 PM.
See you soon, Ilaria Lucardesi and Luigi Forcella
--------------------------------------------- Title: Some isoperimetric inequality involving the boundary momentum and curvature integrals
Abstract: The aim of this talk is twofold. In the first part we deal with a shape optimization problem of a functional involving the boundary momentum. It is known that in dimension two the ball is a maximizer among simply connected sets, when the perimeter and centroid is fixed. In higher dimensions the same result does not hold and we consider a new scaling invariant functional that might be a good candidate to generalize the bidimensional case. For this functional we prove that the ball is a stable maximizer in the class of nearly spherical sets in any dimension. In the second part we focus on a functional involving a weighted curvature integral and the quermassintegrals. We prove upper and lower bounds for this functional in the class of convex sets, which provide a stronger form of the classical Aleksandrov-Fenchel inequality involving the $(n-1)$ and $(n-2)$-quermassintegrals, and consequently a stronger form of the classical isoperimetric inequality in the planar case.