Sweeping out sectional curvature
arXiv:1106.3736 · doi:10.2140/gt.2014.18.617
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.
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