3 papers
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…
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…
math.DG2025
Singular metrics with nonnegative scalar curvature and RCD
Xianzhe Dai, Changliang Wang, Lihe Wang +1
We show that a uniformly Euclidean metric with isolated singularity on , where or , spin, and nonnegative scalar curvature on the s…