English

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

R2 v1 2026-06-21T16:02:24.951Z