Sweeping out sectional curvature
Differential Geometry
2020-10-20 v7
Abstract
We observe that the maximal open set of constant curvature k in a Riemannian manifold with curvature bounded below or above by k has a convexity type property, which we call "two-convexity". This statement is used to prove a number of rigidity statements in comparison geometry.
Cite
@article{arxiv.1106.3736,
title = {Sweeping out sectional curvature},
author = {D. Panov and A. Petrunin},
journal= {arXiv preprint arXiv:1106.3736},
year = {2020}
}
Comments
+minor corrections