  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].
