Rigidity phenomena involving scalar curvature
Differential Geometry
2011-11-22 v3 Mathematical Physics
Analysis of PDEs
math.MP
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.
Keywords
Cite
@article{arxiv.1008.3097,
title = {Rigidity phenomena involving scalar curvature},
author = {S. Brendle},
journal= {arXiv preprint arXiv:1008.3097},
year = {2011}
}
Comments
Final version, to appear in Surveys in Differential Geometry vol. XVI