• Corpus ID: 244773545

Hyperbolic energy and Maskit gluings

@inproceedings{Chrusciel2021HyperbolicEA,
  title={Hyperbolic energy and Maskit gluings},
  author={Piotr T. Chru'sciel and Erwann Delay and Raphaela Wutte},
  year={2021}
}
We derive a formula for the energy of asymptotically locally hyperbolic (ALH) manifolds obtained by a gluing at infinity of two ALH manifolds. As an application we show that there exist three dimensional conformally compact ALH manifolds without boundary, with connected conformal infinity of higher genus, with constant negative scalar curvature and with negative mass. 

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SHOWING 1-10 OF 48 REFERENCES
Gluing constructions for asymptotically hyperbolic manifolds with constant scalar curvature
We show that asymptotically hyperbolic initial data satisfying smallness conditions in dimensions $n\ge 3$, or fast decay conditions in $n\ge 5$, or a genericity condition in $n\ge 9$, can be
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 spherical
Maskit combinations of Poincaré–Einstein metrics
Computing Asymptotic Invariants with the Ricci Tensor on Asymptotically Flat and Asymptotically Hyperbolic Manifolds
We prove in a simple and coordinate-free way the equivalence between the classical definitions of the mass or of the center of mass of an asymptotically flat manifold and their alternative
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. Using
Exotic hyperbolic gluings
We carry out “exotic gluings” a la Carlotto-Schoen for asymptotically hyperbolic general relativistic initial data sets. In particular we obtain a direct construction of non-trivial initial data sets
The hyperbolic positive energy theorem
We show that the causal-future-directed character of the energy-momentum vector of $n$-dimensional asymptotically hyperbolic Riemannian manifolds with spherical conformal infinity, $n\ge 3$, can be
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 so
Curvature and uniformization
We approach the problem of uniformization of general Riemann surfaces through consideration of the curvature equation, and in particular the problem of constructing Poincaré metrics (i.e., complete
Renormalized volume on the Teichm\"uller space of punctured surfaces
We define and study the renormalized volume for geometrically finite hyperbolic $3$-manifolds, including with rank-$1$ cusps. We prove a variation formula, and show that for certain families of
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