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.
Care tutte, cari tutti,
mercoledì 24 gennaio alle ore 17:00, in Sala Riunioni, per il seminario di Analisi Matematica, avremo il piacere di ascoltare Giulia Bevilacqua (Dipartimento di Matematica, Università di Pisa), che terrà un seminario dal titolo “A capillarity approach for the regularity of soap films”. Trovate qui sotto l’abstract. Il seminario sarà preceduto da una merenda, nella stessa aula, dalle ore 16:30.
Il seminario successivo sarà di Tohru Ozawa (Weseda University) venerdì 2 febbraio alle 17.
A presto, Ilaria Lucardesi e Luigi Forcella
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Dear all, On Wednesday 24th at 5:00 PM, in "Sala Riunioni", for the Mathematical Analysis Seminar, we will have the pleasure of listening to Giulia Bevilacqua (Math Department, University of Pisa). The title of the talk is “ A capillarity approach for the regularity of soap films”. Please find below the abstract. The seminar will be preceded by a snack in the same room, starting at 4:30 PM.
The next seminar will be by Tohru Ozawa (Weseda University) on Friday February 2nd at 5PM.
See you soon, Ilaria Lucardesi and Luigi Forcella
--------------------------------------------- Title: A capillarity approach for the regularity of soap films
Abstract: We characterize boundary regularity for a specific variational soap film model. Inspired by [1], soap films are chosen to be sets of finite perimeter containing a fixed volume and satisfying a topological spanning condition. In this talk [2], for a planar curve as the midline of the tubular neighborhood, we show that minimizers are normal smooth graphs with constant mean curvature constructed over the plane and forming on the tubular neighborhood a contact angle equal to $\pi/2$. This is a joint work with Salvatore Stuvard (UNIMI) and Bozhidar Velichkov (UNIPI).
References: [1] D. King, F. Maggi, S. Stuvard: Plateau’s problem as a singular limit of capillarity problems, Communications on Pure and Applied Mathematics, 75:5 2022, pp. 895-969. [2] G. Bevilacqua, S. Stuvard, B. Velichkov: Regularity of a free-boundary Plateau problem, in preparation.
analysis-seminar@lists.dm.unipi.it
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Ilaria Lucardesi