arXiv subjects

Xiaoshang Jin

Publications and source records attributed to Xiaoshang Jin.

22 records · Page 2Linked to original sources

arXiv2023

Rigidity for inscribed radius estimate of asymptotically hyperbolic Einstein manifold

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 upper bound can be achieved only in space form. In this paper, we generalize this result to asymptotically hyperbolic Einstein manifold. We get an upper bound of the relative volume of AH manifold and if we combine it with the recent work of Wang and Zhou, then the rigidity is obtained.

math.DG↗

arXiv2021

Boundary Estimate of Asymptotically Hyperbolic Einstein Manifolds of Even Dimension

In this paper, we study the finite boundary regularity and estimates of an asymptotically hyperbolic Einstein manifold in even dimension $n+1.$ We show that if the initial compactification is $C^{n-1}$ and the $(n-3)$-th derivative of its scalar curvature is Hölder continuous, then the AHE metric is $C^{m,α}$ conformally compact provided the boundary metric is $C^{m,α}$. This is an improvement of Helliwell's result. We also provide an estimate of the Yamabe compactification metric in the new structure.

math.DG↗

arXiv2020

Finite Boundary Regularity for Conformally Compact Einstein Manifolds of Dimension 4

We prove that a $4-$dimensional $C^2$ conformally compact Einstein manifold with Hölder continuous scalar curvature and with $C^{m,α}$ boundary metric has a $C^{m,α}$ compactification. We also study the regularity of the new structure and the new defining function. This is a supplementary proof of Anderson's work and an improvement of Helliwell's result in dimension 4.

math.DG↗

arXiv2018

Boundary Regularity for Asymptotically Hyperbolic Metrics with Smooth Weyl Curvature

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 Michael Anderson's method, we show that $C^{m,α}$ conformally compact Riemannian metrics with Einstein equation vanishing to finite order near boundary have conformal compactifications that are $C^{m+2,α}$ up to the boundary when Weyl curvature is in $C^{m,α}$ and the boundary metric is in $C^{m+2,α}$ where $m\geq 3.$

math.DG↗