Eigenvalue Estimates on Bakry-Emery Manifolds

Autor:	Charalambous, Nelia, Lu, Zhiqin, Rowlett, Julie
Rok vydání:	2020
Předmět:	Mathematics - Spectral Theory Mathematics - Analysis of PDEs Mathematics - Differential Geometry
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
Externí odkaz:	http://arxiv.org/abs/2012.06489 Zobrazit plný text záznamu View this record from Arxiv