On a Conjecture of Ashbaugh and Benguria about Lower Eigenvalues of the Neumann Laplacian

2018/08/28 by Qiaoling Wang, Changyu Xia, Wang, Qiaoling +1 · 2 citations
Computer Science · Mathematics · #35P15 #53C40 #58C40 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1808.09520

openalex publication_date 2018/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove an isoperimetric inequality for lower order eigenvalues of the free membrane problem on bounded domains of a Euclidean space or a hyperbolic space which strengthens the well-known Szegö-Weinberger inequality and supports strongly an important conjecture of Ashbaugh-Benguria.

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• Sharp shifted reciprocal sums of Neumann eigenvalues on space forms
• Sharp inequalities for Neumann eigenvalues on the sphere

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