First Eigenvalue of Jacobi operator and Rigidity Results for Constant Mean Curvature Hypersurfaces

Marcio Batista, Marcos P. Cavalcante, Luiz R. Melo

In this paper, we obtain geometric upper bounds for the first eigenvalue ${\lambda }_1(J)$ of the Jacobi operator for both closed hypersurfaces and compact hypersurfaces with boundary havin…