10 citations · 11 across the 12 of their papers we have counts for
12 papers · 1 filter
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…
The classical Weyl law for Schrödinger operators on complete Riemannian manifolds
Maxim Braverman, Xianzhe Dai, Junrong Yan
We establish a criterion for the validity of the classical (non-semiclassical) Weyl law for Schrödinger operators on complete Riemannian manifolds. In contrast to existin…
Adiabatic Limit and Analytic Torsion of Vector Bundles
Xianzhe Dai, Debin Liu
For a vector bundle over a closed manifold with even and odd, we equip the metric with an adiabatic parameter, and prove that the index of is the same a…
Degeneration of Riemann surfaces and small eigenvalues of the Laplacian
Xianzhe Dai, Ken-Ichi Yoshikawa
For a one-parameter degeneration of compact Riemann surfaces endowed with the Kähler metric induced from the Kähler metric on the total space of the family, we determine the exact…
Weyl Law for Schrödinger Operators on Noncompact Manifolds, Heat Kernel, and Karamata-Hardy-Littlewood Theorem
Xianzhe Dai, Junrong Yan
Building on our earlier work on heat kernel asymptotics for Schrödinger-type operators on noncompact manifolds, we establish both the classical and semiclassical Weyl laws for Schr…
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…
Positive scalar curvature and isolated conical singularity
Xianzhe Dai, Yukai Sun, Changliang Wang
We prove a Geroch type result for isolated conical singularity. Namely, we show that there is no Riemannian metric on with an isolated conical singularity which ha…
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),…
Positive mass theorem for asymptotically flat manifolds with isolated conical singularities
Xianzhe Dai, Yukai Sun, Changliang Wang
We prove the positive mass theorem for asymptotical flat (AF for short) manifolds with finitely many isolated conical singularities. We do not impose the spin condition. Instead we…
Positive mass theorem for asymptotically flat spin manifolds with isolated conical singularities
Xianzhe Dai, Yukai Sun, Changliang Wang
There has been a lot of interests in Positive Mass Theorems for singular metrics on smooth manifolds. We prove a positive mass theorem for asymptotically flat (AF) spin manifolds w…
Singular Weyl's law with Ricci curvature bounded below
Xianzhe Dai, Shouhei Honda, Jiayin Pan +1
We establish two surprising types of Weyl's laws for some compact /Ricci limit spaces. The first type could have power growth of any order (bigger than one). Th…