Universal inequalities on complete noncompact smooth metric measure spaces

Li, Yanli; Feng, Du

doi:10.1007/s00013-017-1099-z

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2021

2024

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Cited by 5 publications

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“…Clearly, the first eigenvalue l 0 has multiplicity one and constant eigenfunction. In recent years, there are some interesting results concerning eigenvalue estimates of the drifting Laplacian and the bi-drifting Laplacian-see, e.g., [9,11,12,15,18,21,22,23,30]. When ðM; h ; iÞ is immersed into the Euclidean N-space ðR N ; canÞ with the canonical metric can, one can define the weighted mean curvature vector as ? , where H is the mean curvature vector of M in R N , ð'f Þ ?…”

Section: Introductionmentioning

confidence: 99%

Estimates for eigenvalues of weighted Laplacian and weighted $p$-Laplacian

et al. 2021

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In this paper, we study two eigenvalue problems of the weighted Laplacian and get the Reilly-type bounds and isoperimetric type bounds for the first nonzero n eigenvalues on hypersurfaces of the Euclidean space. Besides, we give lower bounds for the first eigenvalue of weighted p-Laplacian on submanifolds with locally bounded weighted mean curvature. Meanwhile, several applications of these estimates have also been given. 0 ¼ l 0 < l 1 a l 2 a Á Á Á " þy:F.

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