Calculus of Variations and Geometric Measure Theory

On shape optimization in the class of constant width bodies

Ilaria Lucardesi (Università di Pisa)

created by orlandi on 23 Apr 2020

30 apr 2020 -- 14:30   [open in google calendar]

Zoom meeting

https:/univr.zoom.usj92065903611 (link to the Zoom meeting session)


Constant width bodies are the compact connected subsets of $\mathbb R^n$ with the following property: the projection on any straight line is a segment with constant length. This can also be expressed saying that two parallel support hyperplanes are always separated by the same distance, independently of their direction. A huge amount of literature has been devoted to these fascinating geometric objects, and the fact that many open problems remain unsolved, in spite of their simple statement, is probably an element of their popularity. In this talk I will present two shape optimization problems in the class: the minimization of the $k$-th eigenvalue of the Dirichlet Laplacian, and, in dimension 2, the minimization of the area under inradius constraint. In both cases, main tools are shape derivatives and numerical methods. These are joint works with A. Henrot and B. Bogosel.