Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature
By Giulio Ciraolo, Alessio Figalli, Francesco Maggi, Matteo Novaga. Journal für die Reine und Angewandte Mathematik, 2015
67 citations recorded by the source corpus.
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 {C^{2}} -distance from a single sphere. The corresponding stability inequality is obtained with a sharp decay rate.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/276a7c6cbc06083546f44d07e26e28ce6e96de49
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In Applied Mathematics
- C. Bucur
- Enrico Valdinoci
- Vicentiu D. Rădulescu
- Giovanni Molica Bisci
- Serena Dipierro
- Binlin Zhang
- Raffaella Servadei
- Mingqi Xiang
In Computational Theory and Mathematics
- C. Bucur
- Enrico Valdinoci
- Vicentiu D. Rădulescu
- Giovanni Molica Bisci
- Raffaella Servadei
- Binlin Zhang
- A. Fiscella
- Serena Dipierro
In Mathematical Physics
- C. Bucur
- Enrico Valdinoci
- Vicentiu D. Rădulescu
- Giovanni Molica Bisci
- Serena Dipierro
- Binlin Zhang
- Mingqi Xiang
- Raffaella Servadei
Citations in the corpus
- Nonlocal Diffusion and Applications (2015, background): “See also [14] for the construction of surfaces with constant mean curvature with the structure of onduloids, and [14] and [29] for the proof that bounded surfaces with constant mean curvature are necessarily spheres (this is the analogue of a celebrated result by Alexandrov for surfaces of constant ”