Isoperimetric inequalities for Neumann eigenvalues on bounded domains in rank-1 symmetric spaces

Yifeng Meng; Kui Wang

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arXiv · 2209.13842

Isoperimetric inequalities for Neumann eigenvalues on bounded domains in rank-1 symmetric spaces

Yifeng Meng·Kui Wang

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Abstract

In this paper, we prove sharp isoperimetric inequalities for lower order eigenvalues of Neumann Laplacian on bounded domains in both compact and noncompact rank-1 symmetric spaces. Our results generalize the work of Wang and Xia for bounded domains in the hyperbolic space [13], and Szeg\"o-Weinberger inequality in rank-1 symmetric spaces obtained by Aithal and Santhanam [1].

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Yifeng Meng, Kui Wang. 2022-09-28. Isoperimetric inequalities for Neumann eigenvalues on bounded domains in rank-1 symmetric spaces. https://arxiv.org/abs/2209.13842

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