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Valentina Franceschi
Lundi 8 octobre 2018
Valentina Franceschi (Université Paris Sud)
Anisotropic soap bubbles.
Résumé :
The aim of this seminar is to present some recent results on a minimal partition problem in the Euclidean plane, relative to a suitable family of anisotropic perimeters and volumes. This amounts to find the best configuration of $m\in \mathbb N$ regions in the plane enclosing given volumes, in order to minimize their total perimeter, where perimeter and volume are defined by two different anisotropic densities. The particular structure of such densities is inspired by a geometric model, called the Grushin plane, that will be presented.
In the first part of the seminar we discuss existence of solutions to the minimal partition problem (ongoing work with Aldo Pratelli - Università di Pisa and Giorgio Stefani - SNS, Pisa). We then conclude by analyzing the particular choices of volume and perimeter associated with the Grushin plane : we present in this framework our candidate solutions for the double bubble problem (joint work with Giorgio Stefani).