Eigenvalue Estimates on Bakry-Emery Manifolds
Autor: | Charalambous, Nelia, Lu, Zhiqin, Rowlett, Julie |
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Rok vydání: | 2020 |
Předmět: | |
Zdroj: | 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 |
Druh dokumentu: | Working Paper |
DOI: | 10.1007/978-3-319-12547-3_2 |
Popis: | 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. Comment: 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) |
Databáze: | arXiv |
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