Eigenvalue comparison on Bakry-Emery manifolds

Details Eigenvalue comparison on Bakry-Emery manifolds Eigenvalue comparison on Bakry-Emery manifolds

2011-11-21

arxiv.org/abs/1111.4967v1

Mathematics

Analysis of PDEs

Scientific paper

We prove a comparison theorem on the first Neumann eigenvalue on Bakry-Emery
manifolds. Examples are constructed to illustrate the sharpness of the result.
A linear explicit lower bound is also proved. We also discuss the asymptotic
sharpness of such a result.

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