A Splitting Theorem for Scalar Curvature
Copyright policy )A Splitting Theorem for Scalar Curvature
AbstractWe show that a Riemannian 3‐manifold with nonnegative scalar curvature is flat if it contains an area‐minimizing cylinder. This scalar‐curvature analogue of the classical splitting theorem of J. Cheeger and D. Gromoll (1971) was conjectured by D. Fischer‐Colbrie and R. Schoen (1980) and by M. Cai and G. Galloway (2000). © 2018 the Authors. Communications on Pure and Applied Mathematics is published by the Courant Institute of Mathematical Sciences and Wiley Periodicals, Inc.
- University of L'Aquila Italy
- College of New Jersey United States
- University of Vienna Austria
Mathematics - Differential Geometry, 2-SPHERES, Riemannian 3-manifold, area-minimizing surface, 3-MANIFOLDS, Rigidity results, RIGIDITY, MASS, splitting theorem for scalar curvature, 101009 Geometrie, Global Riemannian geometry, including pinching, nonnegative scalar curvature, Differential Geometry (math.DG), 101009 Geometry, FOS: Mathematics, MINIMAL-SURFACES
Mathematics - Differential Geometry, 2-SPHERES, Riemannian 3-manifold, area-minimizing surface, 3-MANIFOLDS, Rigidity results, RIGIDITY, MASS, splitting theorem for scalar curvature, 101009 Geometrie, Global Riemannian geometry, including pinching, nonnegative scalar curvature, Differential Geometry (math.DG), 101009 Geometry, FOS: Mathematics, MINIMAL-SURFACES
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