Speaker
Dorin Bucur
(Université Savoie Mont Blanc)
Description
Let $\Omega \subset \mathbb{R}^d$ be a set with finite Lebesgue measure such that, for a fixed radius $r>0$, the Lebesgue measure of $\Omega \cap B _ r (x)$ is equal to a positive constant when $x$ varies in the essential boundary of $\Omega$. We prove that $\Omega$ 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 Fragalà.
Primary authors
Dorin Bucur
(Université Savoie Mont Blanc)
Ilaria Fragalà
