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arXiv 2012.06489math.SPmath.APmath.DG

Eigenvalue Estimates on Bakry-Emery Manifolds

Nelia Charalambous, Zhiqin Lu, Julie Rowlett

备注：
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)
发表信息：
In: Escher J., Schrohe E., Seiler J., Walker C. (eds) Elliptic and Parabolic Equations. Springer Proceedings in Mathematics & Statistics, vol 119. Springer, Cham. (2015) 45-61
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英文摘要：

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.

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