Eigenvalues of the bi-drifting Laplacian on the complete noncompact Riemannian manifolds

Li, Xinyang; Mao, Jing; Zeng, Lingzhong

doi:10.1007/s00033-022-01876-9

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2024

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Cited by 6 publications

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“…More results on the clamped plate problem of the drifting Laplacian can be found in [17,46,47,48,49,50,29] and related references therein. In conclusion, the study of the universal inequality for eigenvalues of the bi-drifting Laplacian is still a very active research field.…”

Section: Introductionmentioning

confidence: 99%

Universal Inequalities for Eigenvalues of a Clamped Plate Problem of the Drifting Laplacian

He,

2024

Bull Braz Math Soc, New Series

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Section: Introductionmentioning

confidence: 99%

Universal Inequalities for Eigenvalues of a Clamped Plate Problem of the Drifting Laplacian

He,

2024

Bull Braz Math Soc, New Series

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Inequalities for eigenvalues of the bi-drifting Laplacian on bounded domains in complete noncompact Riemannian manifolds and related results

He,

2024

Annali di Matematica

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Sharp spectral gap estimates for higher-order operators on Cartan–Hadamard manifolds

Farkas,

Kajántó,

Kristály

2024

Commun. Contemp. Math.

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The goal of this paper is to provide sharp spectral gap estimates for problems involving higher-order operators (including both the clamped and buckling plate problems) on Cartan–Hadamard manifolds. The proofs are symmetrization-free — thus no sharp isoperimetric inequality is needed — based on two general, yet elementary functional inequalities. The spectral gap estimate for clamped plates solves a sharp asymptotic problem from [Q.-M. Cheng and H. Yang, Universal inequalities for eigenvalues of a clamped plate problem on a hyperbolic space, Proc. Amer. Math. Soc. 139(2) (2011) 461–471] concerning the behavior of higher-order eigenvalues on hyperbolic spaces, and answers a question raised in [A. Kristály, Fundamental tones of clamped plates in nonpositively curved spaces, Adv. Math. 367(39) (2020) 107113] on the validity of such sharp estimates in high-dimensional Cartan–Hadamard manifolds. As a byproduct of the general functional inequalities, various Rellich inequalities are established in the same geometric setting.

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Eigenvalues of the bi-drifting Laplacian on the complete noncompact Riemannian manifolds

Cited by 6 publications

References 35 publications

Universal Inequalities for Eigenvalues of a Clamped Plate Problem of the Drifting Laplacian

Universal Inequalities for Eigenvalues of a Clamped Plate Problem of the Drifting Laplacian

Inequalities for eigenvalues of the bi-drifting Laplacian on bounded domains in complete noncompact Riemannian manifolds and related results

Sharp spectral gap estimates for higher-order operators on Cartan–Hadamard manifolds

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