A note on the first eigenvalue of spherically symmetric manifolds

Details A note on the first eigenvalue of spherically symmetric manifolds A note on the first eigenvalue of spherically symmetric manifolds

2006-09-18

arxiv.org/abs/math/0609495v1

Mathematics

Differential Geometry

6 pages. We apply Barta's Theorem to give lower and upper bounds for the first eigenvalue of geodesic balls in spherically sym

Scientific paper

We give lower and upper bounds for the first eigenvalue of geodesic balls in
spherically symmetric manifolds. These lower and upper bounds are
$C^{0}$-dependent on the metric coefficients. It gives better lower bounds for
the first eigenvalue of spherical caps than those from Betz-Camera-Gzyl.

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