An Extension of Barta's Theorem and Geometric Applications
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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
23 pages. This paper is an improved version of our paper of the same Titled posted here