A note on the first eigenvalue of spherically symmetric manifolds
Differential Geometry
2011-02-19 v1 Analysis of PDEs
Abstract
We give lower and upper bounds for the first eigenvalue of geodesic balls in spherically symmetric manifolds. These lower and upper bounds are -dependent on the metric coefficients. It gives better lower bounds for the first eigenvalue of spherical caps than those from Betz-Camera-Gzyl.
Cite
@article{arxiv.math/0609495,
title = {A note on the first eigenvalue of spherically symmetric manifolds},
author = {Cleon S. Barroso and G. Pacelli Bessa},
journal= {arXiv preprint arXiv:math/0609495},
year = {2011}
}
Comments
6 pages. We apply Barta's Theorem to give lower and upper bounds for the first eigenvalue of geodesic balls in spherically symmetric manifolds