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arXiv:1106.3736 [math.DG]AbstractReferencesReviewsResources

Sweeping out sectional curvature

D. Panov, A. Petrunin

Published 2011-06-19, updated 2020-10-17Version 7

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.

Comments: +minor corrections
Journal: Geom. Topol. 18 (2014) 617-631
Categories: math.DG
Subjects: 53C20, 53C24
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