Quantitative stability for hypersurfaces with almost constant mean curvature in the hyperbolic space
Articolo
Data di Pubblicazione:
2020
Citazione:
Quantitative stability for hypersurfaces with almost constant mean curvature in the hyperbolic space / G. Ciraolo, L. Vezzoni. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - 69:4(2020), pp. 1105-1153. [10.1512/iumj.2020.69.7952]
Abstract:
We provide sharp stability estimates for the Alexandrov Soap Bubble Theorem in the hyperbolic space. The closeness to a single sphere is quantified in terms of the dimension, the measure of the hypersurface and the radius of the touching ball condition. As consequence, we obtain a new pinching result for hypersurfaces in the hyperbolic space. Our approach is based on the method of moving planes. In this context we carefully review the method and we provide the first quantitative study in the hyperbolic space.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Alexandrov soap bubble theorem; Hyperbolic geometry; Mean curvature; Method of moving planes; Pinching; Stability
Elenco autori:
G. Ciraolo, L. Vezzoni
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