1 citations · 1 across the 3 of their papers we have counts for
4 papers
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…
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…
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…
Volume entropy and rigidity for RCD-spaces
Chris Connell, Xianzhe Dai, Jesús Núñez-Zimbrón +3
We develop the barycenter technique of Besson--Courtois--Gallot so that it can be applied on RCD metric measure spaces. Given a continuous map from a non-collapsed RCD$(-(N-1),…