Reverse Faber-Krahn inequality for the p-Laplacian in hyperbolic space

In this paper, we study the shape optimization problem for first eigenvalue of p-Laplace operator with mixed Neumann-Dirichlet boundary conditions on multiply-connected domains in hyperbolic space. Precisely, establish that among all a given volume and prescribed (n−1)-th quermassintegral convex Dirichlet (inner boundary), concentric annular region produces largest eigenvalue. We also derive Nagy's type inequality outer parallel sets domain