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arXiv · 1808.09520

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

Qiaoling Wang·Changyu Xia
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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 Szeg\"o-Weinberger inequality and supports strongly an important conjecture of Ashbaugh-Benguria.

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Qiaoling Wang, Changyu Xia. 2018-08-28. On a Conjecture of Ashbaugh and Benguria about Lower Eigenvalues of the Neumann Laplacian. https://arxiv.org/abs/1808.09520

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