Deformation of scalar curvature and volume
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Publication:382316
DOI10.1007/s00208-013-0903-8zbMath1278.53041arXiv1211.6168OpenAlexW2061945144MaRDI QIDQ382316
Justin Corvino, Michael Eichmair, Pengzi Miao
Publication date: 18 November 2013
Published in: Mathematische Annalen (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1211.6168
Critical metrics (58E11) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)
Related Items (39)
The general relativistic constraint equations ⋮ STATIC AND RELATED CRITICAL SPACES WITH HARMONIC CURVATURE AND THREE RICCI EIGENVALUES ⋮ Geometric inequalities for critical metrics of the volume functional ⋮ Geometry of compact quasi-Einstein manifolds with boundary ⋮ Einstein-type structures, Besse's conjecture, and a uniqueness result for a \(\varphi \)-CPE metric in its conformal class ⋮ Vacuum Einstein field equations in smooth metric measure spaces: the isotropic case* ⋮ On the geometry of Einstein-type manifolds with some structural conditions ⋮ Volume comparison with respect to scalar curvature ⋮ Deformation of the weighted scalar curvature ⋮ On the \(\sigma_2\)-curvature and volume of compact manifolds ⋮ New gap results on n‐dimensional static manifolds ⋮ Geometry of static perfect fluid space-time ⋮ Critical metrics of the volume functional on three‐dimensional manifolds ⋮ On the volume functional of compact manifolds with harmonic Weyl tensor ⋮ Brown-York mass and positive scalar curvature. II: Besse's conjecture and related problems ⋮ The seed-to-solution method for the Einstein constraints and the asymptotic localization problem ⋮ Multi-localized time-symmetric initial data for the Einstein vacuum equations ⋮ Conformally variational Riemannian invariants ⋮ Smooth scalar curvature decrease of big scale on a sphere ⋮ The prescribed scalar curvature problem for metrics with unit total volume ⋮ Four-dimensional static and related critical spaces with harmonic curvature ⋮ Numerical initial data deformation exploiting a gluing construction: I. Exterior asymptotic Schwarzschild ⋮ Static perfect fluid space-time on compact manifolds ⋮ Remarks on compact quasi-Einstein manifolds with boundary ⋮ Critical metrics of the volume functional on compact three-manifolds with smooth boundary ⋮ On the \(P\)-scalar curvature ⋮ Volume functional of compact 4-manifolds with a prescribed boundary metric ⋮ Isoperimetric inequality and Weitzenböck type formula for critical metrics of the volume ⋮ Causal geodesic incompleteness of spacetimes arising from IMP gluing ⋮ Remarks on critical metrics of the scalar curvature and volume functionals on compact manifolds with boundary ⋮ Localized deformation for initial data sets with the dominant energy condition ⋮ Weakly Einstein critical metrics of the volume functional on compact manifolds with boundary ⋮ Critical metrics on 4-manifolds with harmonic anti-self dual Weyl tensor ⋮ Conformal vector fields and the de-Rham Laplacian on a Riemannian manifold with boundary ⋮ Three-dimensional Ricci-degenerate Riemannian manifolds satisfying geometric equations ⋮ Critical metrics and curvature of metrics with unit volume or unit area of the boundary ⋮ Deformations of \(Q\)-curvature. II. ⋮ Critical metrics of the volume functional on manifolds with boundary ⋮ Bach-flat critical metrics of the volume functional on 4-dimensional manifolds with boundary
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