261 research outputs found
The isoperimetric inequality on asymptotically flat manifolds with nonnegative scalar curvature
In this note, we consider the isoperimetric inequality on an asymptotically
flat manifold with nonnegative scalar curvature, and improve it by using
Hawking mass. We also obtain a rigidity result when equality holds for the
classical isoperimetric inequality on an asymptotically flat manifold with
nonnegative scalar curvature.Comment: Final version, to appear International Mathematics Research Notices.
12 pages, no figure
Rigidity of Asymptotically Hyperboblic 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 and a volume
comparison theorem.Comment: 16 page
Asymptotically hyperbolic metrics on the unit ball with horizons
In this paper, we construct a family of asymptotically hyperbolic manifolds
with horizons and with scalar curvature equal to -6. The manifolds we
constructed can be arbitrary close to anti-de Sitter-Schwarzschild manifolds at
infinity. Hence, the mass of our manifolds can be very large or very small. The
main arguments we used in this paper is gluing methods which was used in
\cite{M}.Comment: 23page
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