An isoperimetric inequality for the harmonic mean of the Steklov eigenvalues in hyperbolic space

Abstract

In this article, we prove an isoperimetric inequality for the harmonic mean of the first $$(n-1)$$ nonzero Steklov eigenvalues on bounded domains in n-dimensional hyperbolic space. Our approach to prove this result also gives a similar inequality for the first n nonzero Steklov eigenvalues on bounded domains in n-dimensional Euclidean space.