Ilaria Lucardesi

Shape optimization under thickness constraint

Among the various width-type constraints considered in shape optimization, the most classical is the maximal width (or diameter), which describes how "large" an admissible set can be. Less commonly studied - but equally significant - is the minimal width, which instead measures the "thickness" of admissible shapes.
In this seminar, I will present some recent results on the optimization, in quantitative form, of the area and the Cheeger constant for sets with prescribed thickness. The talk is based on joint works with Davide Zucco (Turin, Italy), Giorgio Saracco (Ferrara, Italy), and Ilias Ftouhi (Nimes, France).