Weinstock inequality in hyperbolic space

Abstract

In this paper, we establish the Weinstock inequality for the first non-zero Steklov eigenvalue on star-shaped mean convex domains in hyperbolic space ${\mathbb{H}}^n$ for $n\ge 4$. In particular, when the domain is convex, our result gives an affirmative answer to Open Question 4.27 in [7] for the hyperbolic space ${\mathbb{H}}^n$ when $n\ge 4$.

18 pages. All comments are welcome