On Perturbations of the Schwarzschild Anti-De Sitter Spaces of Positive Mass

@article{Ambrozio2014OnPO,
  title={On Perturbations of the Schwarzschild Anti-De Sitter Spaces of Positive Mass},
  author={Lucas C. Ambrozio},
  journal={Communications in Mathematical Physics},
  year={2014},
  volume={337},
  pages={767-783}
}
  • L. Ambrozio
  • Published 18 February 2014
  • Physics, Mathematics
  • Communications in Mathematical Physics
In this paper we prove the Penrose inequality for metrics that are small perturbations of the Schwarzschild anti-de Sitter metrics of positive mass. We use the existence of a global foliation by weakly stable constant mean curvature spheres and the monotonicity of the Hawking mass. 
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References

SHOWING 1-10 OF 24 REFERENCES
Existence and uniqueness of constant mean curvature foliation of asymptotically hyperbolic 3-manifolds II
Abstract In a previous paper, the authors showed that metrics which are asymptotic to Anti-de Sitter-Schwarzschild metrics with positive mass admit a unique foliation by stable spheres with constantExpand
Existence and Uniqueness of Constant Mean Curvature Foliation of Asymptotically Hyperbolic 3-Manifolds
We prove existence and uniqueness of foliations by stable spheres with constant mean curvature for 3-manifolds which are asymptotic to anti-de Sitter–Schwarzschild metrics with positive mass. TheseExpand
The Penrose Inequality for Asymptotically Locally Hyperbolic Spaces with Nonpositive Mass
In the asymptotically locally hyperbolic setting it is possible to have metrics with scalar curvature ≥ −6 and negative mass when the genus of the conformal boundary at infinity is positive. UsingExpand
A Volume Comparison Theorem for Asymptotically Hyperbolic Manifolds
We define a notion of renormalized volume of an asymptotically hyperbolic manifold. Moreover, we prove a sharp volume comparison theorem for metrics with scalar curvature at least −6. Finally, weExpand
ON ISOPERIMETRIC SURFACES IN GENERAL RELATIVITY
We obtain the isoperimetric profile for the standard initial slices in the Reissner‐Nordstrom and Schwarzschild anti-de Sitter spacetimes, following recent work of Bray and Morgan on isoperimetricExpand
The Mass of Asymptotically Hyperbolic Manifolds
Motivated by certain problems in general relativity and Riemannian geometry, we study manifolds which are asymptotic to the hyperbolic space in a certain sense. It is shown that an invariant, the soExpand
The Penrose inequality in general relativity and volume comparison theorems involving scalar curvature (thesis)
In this thesis we describe how minimal surface techniques can be used to prove the Penrose inequality in general relativity for two classes of 3-manifolds. We also describe how a new volumeExpand
The mass of asymptotically hyperbolic Riemannian manifolds
We present a set of global invariants, called mass integrals, which can be defined for a large class of asymptotically hyperbolic Riemannian manifolds. When the boundary at infinity has sphericalExpand
The inverse mean curvature flow and the Riemannian Penrose Inequality
Let M be an asymptotically flat 3-manifold of nonnegative scalar curvature. The Riemannian Penrose Inequality states that the area of an outermost minimal surface N in M is bounded by the ADM mass mExpand
Large Isoperimetric Regions in Asymptotically Hyperbolic Manifolds
We show the existence of isoperimetric regions of sufficiently large volumes in general asymptotically hyperbolic three manifolds. Furthermore, we show that large coordinate spheres are uniquelyExpand
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