English

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