Weinstock inequality in hyperbolic space II

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 $n\ge 3$. We note that when $n\ge 4$, the result was obtained in our previous paper [23]. In particular, when the domain is convex, our result gives an affirmative answer to Open Question 4.27 in [13] for the hyperbolic case.

To appear in Proceedings of the Tenth International Congress of Chinese Mathematicians