“Minimal bubble clusters in the plane with double density”
Lunedì 9 Dicembre 2019, ore 11:00 - Aula 2AB45 - Valentina Franceschi (Sorbonne Université, Parigi)
We present some results about minimal bubble clusters in the plane with double density. 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 suitable densities. We focus on a particular structure of such densities, which is inspired by a sub-Riemannian model, called the Grushin plane. After an overview concerning existence of minimizers, we focus on their Steiner regularity, i.e., the fact that their boundaries are made of regular curves meeting at 120 degrees. We will show that this holds in a wide generality. Although our initial motivation came from the study of the particular sub-Riemannian framework of the Grushin plane, our approach works in wide generality and is new even in the classical Euclidean case.