Address: Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, Campina Grande, Paraíba, Brazil 58109-970
E-mail:
henrique@dme.ufcg.edu.br
marcolazarovelasquez@gmail.com
Abstract: In this paper we study the $r$-stability of closed hypersurfaces with constant $r$-th mean curvature in Riemannian manifolds of constant sectional curvature. In this setting, we obtain a characterization of the $r$-stable ones through of the analysis of the first eigenvalue of an operator naturally attached to the $r$-th mean curvature.
AMSclassification: primary 53C42; secondary 53B30, 53C50, 53Z05, 83C99.
Keywords: space forms, $r$-th mean curvatures, $r$-stability.