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math.DG2026
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 be a bounded smooth horoconvex domain and let be its first Dirichlet eigenfunction. We prove that \[ \operatorname{Hess}_{\mathbb H^2}(-\logψ_1)>0…
math.DG2026
A Large-Diameter Fundamental-Gap Lower Bound for Horoconvex Domains
Xianzhe Dai, John Ennis, Xuan Hien Nguyen +1
We prove a large-diameter fundamental-gap lower bound for compact horoconvex domains in real hyperbolic space of curvature \(-1\). The geometric part reduces large horoconvex domai…