An Extension of Barta's Theorem and Geometric Applications

G. Pacelli Bessa; J. Fabio Montenegro

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An Extension of Barta's Theorem and Geometric Applications

G. Pacelli Bessa·J. Fabio Montenegro

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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.

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BibTeX RIS

G. Pacelli Bessa, J. Fabio Montenegro. 2005-06-16. An Extension of Barta's Theorem and Geometric Applications. https://arxiv.org/abs/math/0308099

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