Plateau-Stein manifolds

DOI10.2478/s11533-013-0387-5zbMath1293.31006arXiv1811.04316OpenAlexW2094831070MaRDI QIDQ2248494

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Publication date: 26 June 2014

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.04316

zbMATH Keywords

Riemannian manifoldsgeometric measure theoryStein manifolds

Mathematics Subject Classification ID

Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Global submanifolds (53C40) Global Riemannian geometry, including pinching (53C20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Potential theory on Riemannian manifolds and other spaces (31C12) Methods of local Riemannian geometry (53B21)

Related Items (12)

Rigidity of mass-preserving 1-Lipschitz maps from integral current spaces into \(\mathbb{R}^n\) ⋮ An extreme limit with nonnegative scalar curvature ⋮ The Sormani–Wenger intrinsic flat convergence of Alexandrov spaces ⋮ Existence of infinitely many minimal hypersurfaces in closed manifolds ⋮ Sewing Riemannian manifolds with positive scalar curvature ⋮ Mean curvature in the light of scalar curvature ⋮ Properties of the Intrinsic Flat Distance ⋮ Dirac and Plateau billiards in domains with corners ⋮ Metric inequalities with scalar curvature ⋮ Existence of minimal hypersurfaces in complete manifolds of finite volume ⋮ Sequences of three dimensional manifolds with positive scalar curvature ⋮ Sobolev bounds and convergence of Riemannian manifolds

Cites Work

• Hilbert volume in metric spaces. I
• The intrinsic flat distance between Riemannian manifolds and other integral current spaces
• Embedding and surrounding with positive mean curvature
• Approximation by positive mean curvature immersions: frizzing
• A local regularity theorem for mean curvature flow
• Ricci curvature of Markov chains on metric spaces
• Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes
• Handlebodies and p-convexity
• The classification of simply connected manifolds of positive scalar curvature
• Lower bounds on Ricci curvature and quantitative behavior of singular sets
• Ricci curvature for metric-measure spaces via optimal transport
• Isoperimetric inequalities of Euclidean type in metric spaces
• Sign and geometric meaning of curvature

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