Caltech/UCLA Joint Analysis Seminar

PLEASE NOTE DIFFERENT TIME

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.