24 citations · 37 across the 7 of their papers we have counts for
8 papers
Existence of static vacuum extensions for Bartnik boundary data near Schwarzschild spheres
Spyros Alexakis, Zhongshan An, Ahmed Ellithy +1
We obtain existence and local uniqueness of asymptotically flat, static vacuum extensions for Bartnik data on a sphere near the data of a sphere of symmetry in a Schwarzschild mani…
Local structure theory of Einstein manifolds with boundary
Zhongshan An, Lan-Hsuan Huang
We study local structure of the moduli space of compact Einstein metrics with respect to the boundary conformal metric and mean curvature. In dimension three, we confirm M. Anderso…
Static vacuum extensions with prescribed Bartnik boundary data near a general static vacuum metric
Zhongshan An, Lan-Hsuan Huang
We introduce the notions of static regular of type (I) and type (II) and show that they are sufficient conditions for local well-posedness of solving asymptotically flat, static va…
New asymptotically flat static vacuum metrics with near Euclidean boundary data
Zhongshan An, Lan-Hsuan Huang
In our prior work toward Bartnik's static vacuum extension conjecture for near Euclidean boundary data, we establish a sufficient condition, called static regular, and confirm larg…
The initial boundary value problem and quasi-local Hamiltonians in General Relativity
Zhongshan An, Michael T. Anderson
We discuss relations between the initial boundary value problem (IBVP) and quasi-local Hamiltonians in GR. The latter have traditionally been based on Dirichlet boundary conditions…
On mass-minimizing extensions of Bartnik boundary data
Zhongshan An
We prove that the space of initial data sets which have fixed Bartnik boundary data and solve the constraint equations is a Banach manifold. Moreover, on this constraint manifold t…
Ellipticity of Bartnik boundary data for stationary vacuum spacetimes
Zhongshan An
We establish a moduli space of stationary vacuum metrics in a spacetime, and set up a well-defined boundary map in , assigning a metric class with its Ba…
Elliptic boundary value problems for the stationary vacuum spacetimes
Zhongshan An
We develop a general method of proving the ellipticity of boundary value problems for the stationary vacuum space time, by showing that the stationary vacuum field equations are el…