Rigidity phenomena involving scalar curvature

Abstract

We give a survey of various rigidity results involving scalar curvature. Many of these results are inspired by the positive mass theorem in general relativity. In particular, we discuss the recent solution of Min-Oo's Conjecture for the hemisphere (cf. [13]). We also analyze the case of equality in Bray's volume comparison theorem.

Final version, to appear in Surveys in Differential Geometry vol. XVI

References in corpus (4)

• Rigidity of area-minimizing two-spheres in three-manifolds
• Scalar curvature rigidity of geodesic balls in S^n
• Scalar Curvature on Compact Symmetric Spaces
• Splitting of 3-Manifolds and Rigidity of Area-Minimising Surfaces

Cited by in corpus (6)

• Spacelike hypersurfaces with negative total energy in de Sitter spacetime
• Geometric inequalities and rigidity theorems on equatorial spheres
• Hypersurfaces with nonnegative scalar curvature
• Scalar curvature rigidity with a volume constraint
• On Brown-York mass and compactly conformal deformations of scalar curvature
• Remarks on a scalar curvature rigidity theorem of Brendle and Marques