Surveys in Differential Geometry

Volume 17 (2012)

Rigidity phenomena involving scalar curvature

Pages: 179 – 202

DOI: http://dx.doi.org/10.4310/SDG.2012.v17.n1.a4

Author

Simon Brendle (Department of Mathematics, Stanford University, 450 Serra Mall, Bldg 380, Stanford, CA 94305)

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. We also analyze the case of equality in Bray’s volume comparison theorem.

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