3 citations · 6 across the 8 of their papers we have counts for
9 papers
Dirichlet eigenvalue asymptotics on conformally compact Einstein manifolds
Xiaoshang Jin
We study the first Dirichlet eigenvalues of large geodesic balls and fixed-width boundary layers on conformally compact Einstein manifolds of dimension For large balls, we d…
Large -Capacitary Invariants, Entropy, and Geometric Rank
Xiaoshang Jin, Jiabin Yin
We introduce large- asymptotic invariants associated with the -capacity, the first -eigenvalue, and the Maz'ya constant on connected complete noncompact Riemannian manifol…
Asymptotic behavior of the first Dirichlet eigenvalue of AHE manifolds
Xiaoshang Jin
In this article, we investigate the rate at which the first Dirichlet eigenvalue of geodesic balls decreases as the radius approaches infinity. We prove that if the conformal infin…
Rigidity for inscribed radius estimate of asymptotically hyperbolic Einstein manifold
Xiaoshang Jin
The inscribed radius of a compact manifold with boundary is bounded above if its Ricci curvature and mean curvature are bounded from below. The rigidity result implies that the upp…
The relative volume function and the capacity of sphere on asymptotically hyperbolic manifolds
Xiaoshang Jin
Following the work of Li-Shi-Qing, we propose the definition of the relative volume function for an AH manifold. It is not a constant function in general and we study the egularity…
Boundary Estimate of Asymptotically Hyperbolic Einstein Manifolds of Even Dimension
Xiaoshang Jin
In this paper, we study the finite boundary regularity and estimates of an asymptotically hyperbolic Einstein manifold in even dimension We show that if the initial compacti…
On compactness conformally compact Einstein manifolds and uniqueness of Graham-Lee metrics, III
Sun-Yung A. Chang, Yuxin Ge, Xiaoshang Jin +1
In this paper, we establish a compactness result for a class of conformally compact Einstein metrics defined on manifolds of dimension . As an application, we derive the gl…
Finite Boundary Regularity for Conformally Compact Einstein Manifolds of Dimension 4
Xiaoshang Jin
We prove that a dimensional conformally compact Einstein manifold with Hölder continuous scalar curvature and with boundary metric has a compactificat…
Boundary Regularity for Asymptotically Hyperbolic Metrics with Smooth Weyl Curvature
Xiaoshang Jin
In this paper, we study the regularity of asymptotically hyperbolic metrics with Einstein condition near boundary and Weyl curvature smooth enough in arbitrary dimension. Following…