• Corpus ID: 246063702

Einstein Type Systems on Complete Manifolds

@inproceedings{Avalos2022EinsteinTS,
  title={Einstein Type Systems on Complete Manifolds},
  author={Rodrigo Avalos and Jorge H. de Lira and Nicolas Marqu{\'e}},
  year={2022}
}
In the present paper, we study the coupled Einstein Constraint Equations (ECE) on complete manifolds through the conformal method, focusing on non-compact manifolds with flexible asymptotics. In particular, we do not impose any specific model for infinity. First, we prove an existence criteria on compact manifolds with boundary which applies to more general systems and can be seen as a natural extension of known existence theory for the coupled ECE. Building on this, we prove an L existence… 

References

SHOWING 1-10 OF 71 REFERENCES

Einstein-Type Elliptic Systems

In this paper we analyse a type of semi-linear systems of partial differential equations which are motivated by the conformal formulation of the Einstein constraint equations coupled with realistic

The Lichnerowicz equation on compact manifolds with boundary

In this paper we initiate a systematic study of the well-posedness theory of the Einstein constraint equations on compact manifolds with boundary. This is an important problem in general relativity,

Rough Solutions of the Einstein Constraints on Closed Manifolds without Near-CMC Conditions

We consider the conformal decomposition of Einstein’s constraint equations introduced by Lichnerowicz and York, on a closed manifold. We establish existence of non-CMC weak solutions using a

The Constraint equations for the Einstein-scalar field system on compact manifolds

We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial

Non-CMC Solutions of the Einstein Constraint Equations on Compact Manifolds with Apparent Horizon Boundaries

In this article we continue our effort to do a systematic development of the solution theory for conformal formulations of the Einstein constraint equations on compact manifolds with boundary. By

Non-CMC solutions to the Einstein constraint equations on asymptotically Euclidean manifolds with apparent horizon boundaries

In this article we further develop the solution theory for the Einstein constraint equations on an n-dimensional, asymptotically Euclidean manifold  ?> with interior boundary Σ. Building on recent

A class of solutions of the vacuum Einstein constraint equations with freely specified mean curvature

We give a sufficient condition, with no restrictions on the mean curvature, under which the conformal method can be used to generate solutions of the vacuum Einstein constraint equations on compact

A Model Problem for Conformal Parameterizations of the Einstein Constraint Equations

We study the conformal and conformal thin sandwich (CTS) methods as candidates for parameterizing the set vacuum initial data for the Cauchy problem of general relativity. To this end we consider a

Sobolev spaces on Riemannian manifolds with bounded geometry: General coordinates and traces

We study fractional Sobolev and Besov spaces on noncompact Riemannian manifolds with bounded geometry. Usually, these spaces are defined via geodesic normal coordinates which, depending on the

Rough solutions of the Einstein constraint equations on compact manifolds

We construct low regularity solutions of the vacuum Einstein constraint equations on compact manifolds. On 3-manifolds we obtain solutions with metrics in Hs where s > 3/2. The constant mean
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