Scalar Curvature Deformation and a Gluing Construction for the Einstein Constraint Equations

By Justin Corvino. 2000

459 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/d20f23680fbfc72b0abb04b5e1fbd8ebddb4dafa

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In Applied Mathematics

In Astronomy and Astrophysics

Citations in the corpus

On the Asymptotics for the Vacuum Einstein Constraint Equations (2003, background): “thematical GR community. In the meantime, P.T. Chru´sciel and E. Delay [CD] have obtained a version of these results as well. Their paper employs our basic techniques (and those of the ﬁrst author in [C]) to give a number of interesting applications; in addition their paper gives an elegant and expl”
The global non-linear stability of the Kerr-de Sitter family of black holes (2016, methodology): “Such localized gluing methods for the constraint equations were first introduced by Corvino [30] for time-symmetric data; this restriction was subsequently removed by Corvino–Schoen [31], and Chruściel–Delay generalized their analysis in [26].”
On mapping properties of the general relativistic constraints operator in weighted function spaces (2003, methodology): “It has been shown by Corvino [27] that there exists a (nonstandard) way of getting a partial improvement on the regularity of solutions.”
Global Existence for the Einstein Vacuum Equations in Wave Coordinates (2003, result): “cular true for a semilinear equation φ= (∂ t )2, [J1]. 5E.g. φ= (∂ t )2 − |∇ x |2 satisﬁes the null-condition. 6The existence of such data is guaranteed by the results of Corvino and Chrusciel-Delay, [Co], [C-D]. 3 has global solutions for all small initial data.7 Here, AJK I,nm(ω) = X |α|=n,|β|=m A”
On the classification of warped product Einstein metrics (2010, background): “The m = 1 case is discussed in [23] and the case where M has no boundary was proved in [30].”
On static three-manifolds with positive scalar curvature (2015, background): “For instance, the left hand side of (1) defines the formal adjoint of the linearisation of the scalar curvature and the existence of static potentials plays an important role in problems related to prescribing the scalar curvature function (see [24], [14] and also [21]).”
Black Hole Remnants and the Information Loss Paradox (2014, background): “…albeit only for metrics that satisfy certain technical assumptions, guarantees that asymptotic observers could not tell the difference: Theorem [Corvino (2000)]: Let g be any smooth, asymptotically flat and scalar-flat metric on Rn, such that the geometry is conformally flat at infinity, with…”
Stability of Black Holes and Black Branes (2012, background): “Proof: The proof of this lemma follows from the (much more general) techniques and results in [4, 5], and also [6].”
Constant mean curvature surfaces in warped product manifolds (2011, background): “of of Theorem 1.1. We note that Riemannian metrics with the property that (∆f)g−D2f+fRic = 0 are called static, and have been studied in connection with questions in general relativity (see e.g. [3], [9], [26]). In Section 3, we prove a sharp inequality for hypersurfaces of positive mean curvature. ”
Further Results on the Smoothability of Cauchy Hypersurfaces and Cauchy Time Functions (2005, methodology): “Even more, some gluing methods to solve Einstein equations make natural to extend a compact spacelike hypersurface with boundary H to a spacelike Cauchy hypersurface S under some restrictions [ 7 , 11]; Theorem 1.1 is then a fundamental claim, valid in general.”
The global stability of the Minkowski space-time in harmonic gauge (2004, methodology): “sumed to coincide with the Schwarzschild data g0ij = (1+ M r )δij, k0ij = 0 in the complement of the ball of radius one centered at the origin. The existence of such data was recently demonstrated in [Co], [C-D]. The stability of Minkowski space-time for the Einstein-vacuum 6At this point, it is unc”
Rigidity and Positivity of Mass for Asymptotically Hyperbolic Manifolds (2007, methodology): “Within the context of the approach taken in this paper, one possible way to accomplish this would be to extend the results of Corvino-Schoen [11, 12] and Chruściel-Delay [9] on initial data deformations to the asymptotically hyperbolic setting.”
An integral formula and its applications on sub-static manifolds (2016, background): “jXiXj under orthnormal frames. It is also well-known that a static Riemannian triple must be of constant scalar curvature and the zero set {V = 0} is a totally geodesic regular hypersurface, see e.g. [9, 7]. 2.1. Local and global warped product spaces. Theclass ofwarped product manifolds always serv”