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

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].