On Carlotto-Schoen-type scalar-curvature gluings

Erwann Delay; Piotr T. Chru\'sciel

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On Carlotto-Schoen-type scalar-curvature gluings

Piotr T. Chruściel, Erwann Delay

Differential Geometry · Submitted 3 Nov 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We carry out a Carlotto-Schoen-type gluing with interpolating scalar curvature on cone-like sets, or deformations thereof, in the category of smooth Riemannian asymptotically Euclidean metrics.

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We carry out a Carlotto-Schoen-type gluing with interpolating scalar curvature on cone-like sets, or deformations thereof, in the category of smooth Riemannian asymptotically Euclidean metrics.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We carry out a Carlotto-Schoen-type gluing with interpolating scalar curvature on cone-like sets, or deformations thereof, in the category of smooth Riemannian asymptotically Euclidean metrics.	contribution 1.00	0.94	0.75	asserted 1.00

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We carry out a Carlotto-Schoen-type gluing with interpolating scalar curvature on cone-like sets, or deformations thereof, in the category of smooth Riemannian asymptotically Euclidean metrics.

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2 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Builds on it 1 paper

As it turns out, the analysis of Carlotto and Schoen can be readily generalised to linearised gravitational fields on cone-like sets as considered in [ref] (compare [ref] ).

Shielding linearised gravity · Introduction · 1.00

What it cites · 11 sentences without a confident label

Builds on 1 paper

* Rather than gluing an asymptotically Euclidean metric to a flat one, any two asymptotically Euclidean metrics $g_1$ and $g_2$ are glued together. * In the spirit of [ref] , the gluings at zero-scalar curvature are replaced by gluings where the scalar curvature of the final metric equals

Localized gluing of Riemannian metrics in interpolating their scalar curvature · Introduction · 0.87

Uses the method or tool of 1 paper

We start by showing that Theorem 3.6 of [ref] with $K≡0 ≡Y$ applies, with $g_0$ taken to be the Euclidean metric.

On mapping properties of the general relativistic constraints operator in weighted function spaces, with applications · Gluing on sets which are scale-invariant at large distances · 0.92

Cites as support 1 paper

(This is essentially [ref] , together with unique continuation for solutions of the KID equation.) So it suffices to show that functions $δN∈k+4g$ are $o(1)$ in some cone contained in $Ω$.

Killing vectors in asymptotically flat space--times: II. Asymptotically translational Killing vectors and the rigid positive energy theorem in higher dimensions · Gluing on sets which are scale-invariant at large distances · 0.98

Cites as background 1 paper

In an outstanding paper [ref] Carlotto and Schoen have constructed non-trivial asymptotically Euclidean scalar-flat metrics which are Minkowskian outside of a solid cone.

Localizing solutions of the Einstein constraint equations · Introduction · 0.80

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