An extension of Barta’s Theorem and geometric applications

By G. Pacelli, Bessa J Fábio Montenegro. 2003

47 citations recorded by the source corpus.

We prove an extension of a theorem of Barta and we give some 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 show that the spectrum of the Nadirashvili bounded minimal surfaces in \(\mathbb{R}^{3}\) have positive lower bounds. We prove a stability theorem for minimal hypersurfaces of the Euclidean space, giving a converse statement of a result of Schoen. Finally we prove generalization of a result of Kazdan–Kramer about existence of solutions of certain quasi-linear elliptic equations.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b604cc94f6b8469b18a8a6bf2dcd7fd1c859fa26

Citations in the corpus

• Eigenvalue Estimates for Submanifolds with Locally Bounded Mean Curvature (2002, unknown): “1) we need the following proposition proved in [5].”