We prove that the boundary of a (not necessarily connected) bounded smooth set with constant nonlocal mean curvature is a sphere. More generally, and in contrast with what happens in the classical case, we show that the Lipschitz constant of the nonlocal mean curvature of such a boundary controls its C2-distance from a single sphere. The corresponding stability inequality is obtained with a sharp decay rate.
|Numero di pagine||20|
|Rivista||JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK|
|Stato di pubblicazione||Published - 2018|
All Science Journal Classification (ASJC) codes
- Applied Mathematics
Ciraolo, G., Figalli, A., Novaga, M., & Maggi, F. (2018). Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 2018, 275-294.