Isoperimetric inequalities for Neumann eigenvalues on bounded domains in rank-1 symmetric spaces
Differential Geometry
2024-03-27 v2 Analysis of PDEs
Spectral Theory
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].
Keywords
Cite
@article{arxiv.2209.13842,
title = {Isoperimetric inequalities for Neumann eigenvalues on bounded domains in rank-1 symmetric spaces},
author = {Yifeng Meng and Kui Wang},
journal= {arXiv preprint arXiv:2209.13842},
year = {2024}
}
Comments
to appear in Calculus of Variations and Partial Differential Equations