# Caltech/UCLA Joint Analysis Seminar

Tuesday, May 4, 2021
10:00am to 10:50am
Online Event
Rigidity results for measurable sets
Dorin Bucur, Laboratoire de Mathématiques, Université de Savoie,

Let Ω ⊂ ℝd be a set with finite Lebesgue measure such that, for a fixed radius r>0, the Lebesgue measure of Ω ∩ Br(x) is equal to a positive constant when x varies in the essential boundary of Ω. We prove that Ω is a ball (or a finite union of equal balls) provided it satisfies a nondegeneracy condition, which holds in particular for any set of diameter larger than r which is either open and connected, or of finite perimeter and indecomposable. This is a joint work with Ilaria Fragala.