Sweeping out sectional curvature

D. Panov, A. Petrunin

Research output: Working paper/PreprintPreprint

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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.
Original languageEnglish
Publication statusPublished - 19 Jun 2011

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