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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

The paper proves that the first Dirichlet eigenfunction on any bounded smooth horoconvex domain in the hyperbolic plane is log‑concave, i.e., the Hessian of its negative logarithm…