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Tuesday, May 04, 2021
10:00 AM - 10:50 AM
Online Event

Caltech/UCLA Joint Analysis Seminar

Rigidity results for measurable sets
Dorin Bucur, Laboratoire de Mathématiques, Université de Savoie,

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.

For more information, please contact Math Department by phone at 626-395-4335 or by email at mathinfo@caltech.edu.