Log-Concavity and Level-Set Horoconvexity of the First Eigenfunction on Horoconvex Domains in the Hyperbolic Plane

Xianzhe Dai, John M. Ennis, Xuan Hien Nguyen +1

Let $\Omega \subset {\mathbb{H}}^2$ be a bounded smooth horoconvex domain and let ${\psi }_1>0$ be its first Dirichlet eigenfunction. We prove that \[ \operatorname{Hess}_{\mathbb H^2}(-\logψ_1)>0…