A half-space type property in the Euclidean sphere
Archivum mathematicum, Tome 58 (2022) no. 1, pp. 49-63.

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We study the notion of strong r-stability for the context of closed hypersurfaces Σn (n3) with constant (r+1)-th mean curvature Hr+1 immersed into the Euclidean sphere Sn+1, where r{1,,n2}. In this setting, under a suitable restriction on the r-th mean curvature Hr, we establish that there are no r-strongly stable closed hypersurfaces immersed in a certain region of Sn+1, a region that is determined by a totally umbilical sphere of Sn+1. We also provide a rigidity result for such hypersurfaces.
DOI : 10.5817/AM2022-1-49
Classification : 53C21, 53C42
Mots-clés : Euclidean sphere; closed hypersurfaces; (r+1)-th mean curvature; strong r-stability; geodesic spheres; upper (lower) domain enclosed by a geodesic sphere
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Velásquez, Marco Antonio Lázaro. A half-space type property in the Euclidean sphere. Archivum mathematicum, Tome 58 (2022) no. 1, pp. 49-63. doi : 10.5817/AM2022-1-49. https://geodesic-test.mathdoc.fr/articles/10.5817/AM2022-1-49/

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