On shape optimization in the class of constant width bodies

Ilaria Lucardesi - Nancy - Lorraine

Date and time
Thursday, April 30, 2020 at 2:30 PM

Contact person
Giandomenico Orlandi

Publication date
April 23, 2020

Computer Science  


Abstract: 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.

link to the Zoom meeting

date : 30 apr. 2020 02:15 PM Rome



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