The region of the unit Euclidean sphere that admits a class of (r,s)-linear Weingarten hypersurfaces
- Autores: Marco Antonio Lázaro Velásquez
- Localización: Selecciones Matemáticas, ISSN-e 2411-1783, Vol. 10, Nº. 2, 2023, págs. 285-298
- Idioma: inglés
- DOI: 10.17268/sel.mat.2023.02.05
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Resumen
In the unit Euclidean sphere Sn+1, we deal with a class of hypersurfaces that were characterized in [23] as the critical points of a variational problem, the so-called (r, s)-linear Weingarten hypersurfaces (0 ≤ r ≤s ≤ n−1); namely, the hypersurfaces of Sn+1 that has a linear combination arHr+1+・ ・ ・+asHs+1 of their higher order mean curvatures Hr+1 and Hs+1 being a real constant, where ar, . . . , ar are nonnegative real numbers (with at least one non zero). By assuming a geometric constraint involving the higher order mean curvatures of these hypersurfaces, we prove a uniqueness result for strongly stable (r, s)-linear Weingarten hypersurfaces immersed in a certain region determined by a geodesic sphere of Sn+1. We also establish a nonexistence result in another region of Sn+1 for strongly stable Weingarten (r, s)-linear hypersurfaces.
