An Extension of Barta's Theorem and Geometric Applications

Abstract

We prove an extension of a theorem of Barta then we make few geometric applications. We extend Cheng's lower eigenvalue estimates of normal geodesic balls. We generalize Cheng-Li-Yau eigenvalue estimates of minimal submanifolds of the space forms. We prove an stability theorem for minimal hypersurfaces of the Euclidean space, giving a converse statement of a result of Schoen. Finally we prove a generalization of a result of Kazdan-Kramer about existence of solutions of certain quasi-linear elliptic equations.

23 pages. This paper is an improved version of our paper of the same Titled posted here

References in corpus (1)

• Eigenvalue estimates for submanifolds with locally bounded mean curvature

Cited by in corpus (2)

• A differential method for bounding the ground state energy
• Upper and lower bounds for an eigenvalue associated with a positive eigenvector