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• W3013588336 abstract "Alexandrov's soap bubble theorem asserts that spheres are the only connected closed embedded hypersurfaces in the Euclidean space with constant mean curvature. The theorem can be extended to space forms and it holds for more general functions of the principal curvatures. In this short review, we discuss quantitative stability results regarding Alexandrov's theorem which have been obtained by the author in recent years. In particular, we consider hypersurfaces having mean curvature close to a constant and we quantitatively describe the proximity to a single sphere or to a collection of tangent spheres in terms of the oscillation of the mean curvature. Moreover, we also consider the problem in a non local setting, and we show that the non local effect gives a stronger rigidity to the problem and prevents the appearance of bubbling." @default.
• W3013588336 created "2020-04-03" @default.
• W3013588336 creator A5056554949 @default.
• W3013588336 date "2020-03-26" @default.
• W3013588336 modified "2023-09-27" @default.
• W3013588336 title "Quantitative estimates for almost constant mean curvature hypersurfaces." @default.
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• W3013588336 hasPublicationYear "2020" @default.
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