Eigenvalue Estimates on Bakry-Emery Manifolds

Nelia Charalambous; Zhiqin Lu; Julie Rowlett

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

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arXiv · 2012.06489

Eigenvalue Estimates on Bakry-Emery Manifolds

Nelia Charalambous·Zhiqin Lu·Julie Rowlett

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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.

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BibTeX RIS

Nelia Charalambous, Zhiqin Lu, Julie Rowlett. 2020-12-11. Eigenvalue Estimates on Bakry-Emery Manifolds. https://doi.org/10.1007/978-3-319-12547-3_2

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