Almost non-negative scalar curvature on Riemannian manifolds conformal to tori

DOI10.1007/s12220-021-00677-2OpenAlexW3092810279WikidataQ115376740 ScholiaQ115376740MaRDI QIDQ2238547

Brian M. Allen

Publication date: 1 November 2021

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.06008

zbMATH Keywords

scalar curvatureYamabe problemgeometric stabilitytoriintrinsic flat convergenceconformal Riemannian manifolds

Mathematics Subject Classification ID

Rigidity results (53C24) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Conformal structures on manifolds (53C18)

Related Items (5)

Conformal tori with almost non-negative scalar curvature ⋮ \(d_p\)-convergence and \(\epsilon\)-regularity theorems for entropy and scalar curvature lower bounds ⋮ Sobolev inequalities and convergence for Riemannian metrics and distance functions ⋮ Kähler tori with almost non-negative scalar curvature ⋮ From \(L^p\) bounds to Gromov-Hausdorff convergence of Riemannian manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The intrinsic flat distance between Riemannian manifolds and other integral current spaces
• A Ricci flow proof of a result by Gromov on lower bounds for scalar curvature
• Conformal deformation of a Riemannian metric to constant scalar curvature
• Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature
• Spin and scalar curvature in the presence of a fundamental group. I
• Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
• Scalar curvature, metric degenerations and the static vacuum Einstein equations on 3-manifolds. I
• Stability of the positive mass theorem for graphical hypersurfaces of Euclidean space
• Stability of graphical tori with almost nonnegative scalar curvature
• Relating notions of convergence in geometric analysis
• Dirac and Plateau billiards in domains with corners
• Contrasting various notions of convergence in geometric analysis
• Intrinsic flat stability of the positive mass theorem for graphical hypersurfaces of Euclidean space
• Warped tori with almost non-negative scalar curvature
• The Yamabe problem
• Scalar Curvature and Intrinsic Flat Convergence

This page was built for publication: Almost non-negative scalar curvature on Riemannian manifolds conformal to tori