Rigidity phenomena involving scalar curvature

Details Rigidity phenomena involving scalar curvature Rigidity phenomena involving scalar curvature

2010-08-18

arxiv.org/abs/1008.3097v3

Mathematics

Differential Geometry

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

Scientific paper

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.

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