New gap results on n‐dimensional static manifolds

DOI10.1002/MANA.201900146zbMath1530.53046OpenAlexW3203772787WikidataQ125989693 ScholiaQ125989693MaRDI QIDQ6073352

Allan G. Freitas

Publication date: 17 October 2023

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.201900146

zbMATH Keywords

static potentialpinching conditionstatic manifoldgap results\(V\)-static manifold

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Global Riemannian geometry, including pinching (53C20) Rigidity results (53C24) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Cites Work

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• Deformation of scalar curvature and volume
• Deformations of the hemisphere that increase scalar curvature
• Convergence and rigidity of manifolds under Ricci curvature bounds
• Vanishing sectional curvature on the boundary and a conjecture of Schroeder and Strake
• On the volume functional of compact manifolds with boundary with constant scalar curvature
• Sur la géométrie d'une généralisation de l'équation différentielle d'Obata
• Existence and structure of past asymptotically simple solutions of Einstein's field equations with positive cosmological constant
• A note on the fundamental group of a compact minimal hypersurface
• A differential equation arising from scalar curvature function
• Ricci curvature, geodesics and some geometric properties of Riemannian manifolds with boundary
• Four-manifolds with \(\delta W^+=0\) and Einstein constants of the sphere.
• On static three-manifolds with positive scalar curvature
• On Einstein four-manifolds with \(S^1\)-actions
• Remarks on critical metrics of the scalar curvature and volume functionals on compact manifolds with boundary
• Uniqueness of the de Sitter spacetime among static vacua with positive cosmological constant
• Compactness of the space of embedded minimal surfaces with free boundary in three-manifolds with nonnegative Ricci curvature and convex boundary
• A remark about static space times
• Einstein and conformally flat critical metrics of the volume functional
• A note on Fischer-Marsden’s conjecture
• Scalar curvature deformation and a gluing construction for the Einstein constraint equations

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