Eigenvalue estimates for the drifting Laplacian and the p-Laplacian on submanifolds of warped products

In this paper, we investigate minimal submanifolds M immersed into warped products of type , where is positive, and can give lower bounds for the weighted fundamental tone of the drifting Laplacian, the first eigenvalue of the p-Laplacian on open domains in M. This achievement enables us to deal wit...

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Bibliographic Details
Published inApplicable analysis Vol. 100; no. 11; pp. 2275 - 2300
Main Authors Lu, Wei, Mao, Jing, Wu, Chuan-Xi, Zeng, Ling-Zhong
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 18.08.2021
Taylor & Francis Ltd
Subjects
Cones
Eigenvalues
Estimates
Euclidean geometry
Hyperspaces
Lower bounds
Manifolds (mathematics)
p-Laplacian
Salvatore Leonardi
spherically symmetric manifolds
the drifting Laplacian
warped products
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Summary:In this paper, we investigate minimal submanifolds M immersed into warped products of type , where is positive, and can give lower bounds for the weighted fundamental tone of the drifting Laplacian, the first eigenvalue of the p-Laplacian on open domains in M. This achievement enables us to deal with spectral estimates for minimal submanifolds bounded by cylinders, cones, spheres and pseudo-hyperbolic spaces, and meanwhile some interesting byproducts can be obtained. For instance, we can show that the fundamental tone of any cylindrically bounded minimal hypersurface in the Euclidean m-space ( ) is positive.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2019.1679793