Eigenvalue Estimates on Bakry-Emery Manifolds
Spectral Theory
2020-12-14 v1 Analysis of PDEs
Differential Geometry
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.
Cite
@article{arxiv.2012.06489,
title = {Eigenvalue Estimates on Bakry-Emery Manifolds},
author = {Nelia Charalambous and Zhiqin Lu and Julie Rowlett},
journal= {arXiv preprint arXiv:2012.06489},
year = {2020}
}
Comments
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)