An Extension of Barta's Theorem and Geometric Applications
Differential Geometry
2008-05-06 v4
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.
Cite
@article{arxiv.math/0308099,
title = {An Extension of Barta's Theorem and Geometric Applications},
author = {G. Pacelli Bessa and J. Fabio Montenegro},
journal= {arXiv preprint arXiv:math/0308099},
year = {2008}
}
Comments
23 pages. This paper is an improved version of our paper of the same Titled posted here