5 Result(s)
-
Article
Open AccessCharacterization of Large Isoperimetric Regions in Asymptotically Hyperbolic Initial Data
Let (M, g) be a complete Riemannian 3-manifold asymptotic to Schwarzschild-anti-deSitter and with scalar curvature \({R \geq - 6}\) ...
-
Article
On Geometric Problems Related to Brown-York and Liu-Yau Quasilocal Mass
We discuss some geometric problems related to the definitions of quasilocal mass proposed by Brown and York (Contemporary mathematics, vol 132, American Mathematical Society, Providence, pp 129–142, 1992; Phys...
-
Article
Quasi-Local Mass and the Existence of Horizons
In this paper, we obtain lower bounds for the Brown-York quasilocal mass and the Bartnik quasilocal mass for compact three manifolds with smooth boundaries. As a consequence, we derive sufficient conditions fo...
-
Article
Rigidity of Asymptotically Hyperbolic Manifolds
In this paper, we prove a rigidity theorem of asymptotically hyperbolic manifolds only under the assumptions on curvature. Its proof is based on analyzing asymptotic structures of such manifolds at infinity an...
-
Article
Quasi-Spherical Metrics and Applications
In this paper, using the idea of Bartnik [B2] on quasi-spherical metrics we continue our study on the boundary behaviors of compact manifolds with nonnegative scalar curvature and nonempty boundary. Unlike the...
