Deformation of scalar curvature and volume

Corvino, Justin; Eichmair, Michael; Miao, Pengzi

doi:10.1007/s00208-013-0903-8

Cited by 73 publications

(121 citation statements)

References 27 publications

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“…This question has been investigated in the work of Chruściel, Corvino, Delay, Eichmair, Isenberg, Maxwell, Mazzeo, Miao, Pollack, and Schoen (see [5], [7], [8], [9], [10], [15], [16], and [17]). Notably, the work of Chruściel-Isenberg-Pollack (CIP) [7]-which builds upon the basic structure of the Isenberg-Mazzeo-Pollack [16] construction and the Corvino [8] and Chruściel-Delay [5] localizing procedure-was used to find examples of spacetimes that do not contain constant mean curvature (CMC) Cauchy surfaces.…”

Section: Introductionmentioning

confidence: 99%

Causal geodesic incompleteness of spacetimes arising from IMP gluing

Burkhart

Pollack

2019

Gen Relativ Gravit

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In 2002, Isenberg-Mazzeo-Pollack (IMP) constructed a series of vacuum initial data sets via a gluing construction. In this paper, we investigate some local geometry of these initial data sets as well as implications regarding their spacetime developments. In particular, we state conditions for the existence of outer trapped surfaces near the center of the IMP gluing neck and thence use a generalization of the Penrose incompleteness theorem to deduce null incompleteness of the resulting spacetimes. Initial data, gluing, outer trapped surfaces, incompleteness

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Section: Introductionmentioning

confidence: 99%

Causal geodesic incompleteness of spacetimes arising from IMP gluing

Burkhart

Pollack

2019

Gen Relativ Gravit

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“…A noter que dans un travail récent [20], J. Corvino, M. Eichmair et P. Miao obtiennent un recollement localisé, à courbure scalaire constante et où le volume total est préservé. Ils montrent ensuite comment ce résultat peut être utilisé pour construire une famille de contre-exemples à la conjecture de Min-Oo sur la rigidité de l'hémisphère S n + .…”

Section: éTude Du Comportement à L'infini De Données Initiales Asymptunclassified

Principe de recollement des équations des contraintes en relativité générale

Cortier

2012

Séminaire De Théorie Spectrale Et Géométrie

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“…It is not clear if it yields a scalar curvature increasing family g t of big scale; refer to the construction of Corvino-Eichmair-Miao in [6].…”

Section: Introductionmentioning

confidence: 98%

Smooth scalar curvature decrease of big scale on a sphere

Kang

Kim

2014

Differential Geometry and its Applications

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Motivated by Lohkamp's conjecture on curvature deformation in [13], we present a local smooth decrease of scalar curvature by big scale on a sphere as follows. Given any positive numbers N , a, b with a < b < π, we obtain a C ∞ -continuous path of Riemannian metrics g t , 0 ≤ t ≤ 1, on the 4-dimensional sphere S 4 , with g 0 being the round metric of constant curvature 1, such that the scalar curvatures s(g t ) are strictly decreasing in t on the open ball B g0 b (p) of g 0 -radius b centered at a point p, s(g 1 ) < −N on B g0 a (p) and g t = g 0 on the complement of the ball B g0 b (p). This result goes beyond what can be done with Corvino's local first-order deformation theory of scalar curvature [5]. Albeit done on a sphere, the argument here seems generalizable to a larger class of metrics.

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Deformation of scalar curvature and volume

Cited by 73 publications

References 27 publications

Causal geodesic incompleteness of spacetimes arising from IMP gluing

Causal geodesic incompleteness of spacetimes arising from IMP gluing

Principe de recollement des équations des contraintes en relativité générale

Smooth scalar curvature decrease of big scale on a sphere

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