Eigenvalue Estimates on Bakry-Emery Manifolds

Nelia Charalambous; Zhiqin Lu; Julie Rowlett

doi:10.1007/978-3-319-12547-3_2

paper

Eigenvalue Estimates on Bakry-Emery Manifolds

arXiv:2012.06489 · doi:10.1007/978-3-319-12547-3_2

Abstract

We demonstrate lower bounds for the eigenvalues of compact Bakry-Emery manifolds with and without boundary. The lower bounds for the first eigenvalue rely on a generalised maximum principle which allows gradient estimates in the Riemannian setting to be directly applied to the Bakry-Emery setting. Lower bounds for all eigenvalues are demonstrated using heat kernel estimates and a suitable Sobolev inequality.

This is a preliminary version of the article by the same name that was subsequently revised and published in the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 119)