Critical metrics of the volume functional on manifolds with boundary

DOI10.1090/proc/13619zbMath1368.53035arXiv1603.02932OpenAlexW2963118665MaRDI QIDQ5270152

Halyson I. Baltazar, Ernani jun. Ribeiro

Publication date: 22 June 2017

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.02932

zbMATH Keywords

critical metricsvolume functionalparallel Ricci tensorharmonic Weyl tensorMiao-Tam critical metric

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Rigidity results (53C24) Critical metrics (58E11) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Manifolds of metrics (especially Riemannian) (58D17)

Related Items (14)

Volume comparison with respect to scalar curvature ⋮ On the \(\sigma_2\)-curvature and volume of compact manifolds ⋮ Critical metrics of the volume functional on three‐dimensional manifolds ⋮ On the volume functional of compact manifolds with harmonic Weyl tensor ⋮ Paracontact metric \((\kappa, \mu)\)-manifold satisfying the Miao-Tam equation ⋮ Critical metrics of the volume functional on compact three-manifolds with smooth boundary ⋮ Volume functional of compact 4-manifolds with a prescribed boundary metric ⋮ Isoperimetric inequality and Weitzenböck type formula for critical metrics of the volume ⋮ Remarks on critical metrics of the scalar curvature and volume functionals on compact manifolds with boundary ⋮ On static manifolds and related critical spaces with cyclic parallel Ricci tensor ⋮ On static manifolds and related critical spaces with zero radial Weyl curvature ⋮ Weakly Einstein critical metrics of the volume functional on compact manifolds with boundary ⋮ Critical metrics with cyclic parallel Ricci tensor for volume functional on manifolds with boundary ⋮ Critical metrics on 4-manifolds with harmonic anti-self dual Weyl tensor

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• Scalar curvature deformation and a gluing construction for the Einstein constraint equations

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