Super Log-concavity of the First Eigenfunctions for Horo-convex Domains in Hyperbolic Space

Guofang Wei, Ling Xiao

In this paper, we prove that the first eigenfunction of the Laplacian for a horo-convex domain $\Omega \subset {\mathbb{H}}^n$ is super log-concave when $\text{diam}(\Omega )$ is not large. Our re…