Isoperimetric bounds for Wentzel-Laplace eigenvalues on Riemannian\n manifolds

2020/05/24 by Aïssatou M. Ndiaye, Ndiaye, Aïssatou M.
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2005.12750

openalex publication_date 2020/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate eigenvalues of the Wentzel-Laplace operator on\na bounded domain in some Riemannian manifold. We prove asymptotically optimal\nestimates, according to the Weyl's law through bounds that are given in terms\nof the isoperimetric ratio of the domain. Our results show that the\nisoperimetric ratio allows to control the entire spectrum of the\nWentzel-Laplace operator in various ambient spaces.\n

Related

• Asymptotically sharp bound for Wentzel-Laplace eigenvalues
• Isoperimetric Bounds for Eigenvalues of the Wentzell-Laplace, the Laplacian and a biharmonic Steklov Problem
• Counter-example to a Kröger type spectral inequality
• Eigenvalues of the Wentzell-Laplace Operator and of the Fourth Order Steklov Problems
• Several isoperimetric inequalities of Dirichlet and Neumann eigenvalues of the Witten-Laplacian