On area comparison and rigidity involving the scalar curvature

DOI10.1007/s12220-014-9550-xzbMath1336.53051arXiv1309.1050OpenAlexW2008724271MaRDI QIDQ254264

Vlad Moraru

Publication date: 8 March 2016

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

Full work available at URL: https://arxiv.org/abs/1309.1050

zbMATH Keywords

scalar curvaturerigidityminimal surfacesconstant mean curvature

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Global Riemannian geometry, including pinching (53C20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (5)

Free boundary hypersurfaces with non-positive Yamabe invariant in mean convex manifolds ⋮ Rigidity results of weighted area-minimizing hypersurfaces ⋮ Area estimates and rigidity of non-compact 𝐻-surfaces in 3-manifolds ⋮ Rigidity of marginally outer trapped (hyper)surfaces with negative 𝜎-constant ⋮ On area comparison and rigidity involving the scalar curvature

Cites Work

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• On area comparison and rigidity involving the scalar curvature
• Rigidity of area-minimizing hyperbolic surfaces in three-manifolds
• On the second derivative of the total scalar curvature
• Surfaces with maximal constant mean curvature
• Rigidity of area-minimizing two-spheres in three-manifolds
• Scalar curvature of a metric with unit volume
• 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
• Volume estimate of submanifolds in compact Riemannian manifolds
• Kodaira dimension and the Yamabe problem
• Rigidity of stable minimal hypersurfaces
• Yamabe constants and the perturbed Seiberg-Witten equations
• Scalar curvature, covering spaces, and Seiberg-Witten theory
• Computations of the Yamabe invariant
• Classification of prime 3-manifolds with \(\sigma\) invariant greater than \(\mathbb RP^3\)
• Four-manifolds without Einstein metrics
• Gradient Schrödinger operators, manifolds with density and applications
• Rigidity of area-minimizing free boundary surfaces in mean convex three-manifolds
• Canonical metrics on 3-manifolds and 4-manifolds
• On the topology and area of higher-dimensional black holes
• A general comparison theorem with applications to volume estimates for submanifolds
• The Yamabe problem
• The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
• The Yamabe invariant of simply connected manifolds
• Recent progress on the Yamabe problem
• Stability and rigidity of extremal surfaces in Riemannian geometry and General Relativity
• Splitting of 3-manifolds and rigidity of area-minimising surfaces
• Riemannian Geometry
• Rigidity of area minimizing tori in 3-manifolds of nonnegative scalar curvature

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