The region of the unit Euclidean sphere that admits a class of (r,s)-linear Weingarten hypersurfaces

• Autor: Lázaro Velásquez, Marco Antonio
• Formato: artículo
• Fecha de Publicación: 2023
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revistas - Universidad Nacional de Trujillo
• Lenguaje: inglés
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/5682
• Enlace del recurso: https://revistas.unitru.edu.pe/index.php/SSMM/article/view/5682
• Nivel de acceso: acceso abierto
• Materia: unit Euclidean space; (r, s)-linear Weingarten hypersurfaces; upper (lower) domain enclosed by the geodesic sphere of unit Euclidean space of level τ0; strong stability; geodesic spheres

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.