Sweeping out sectional curvature

Dmitri Panov; Anton Petrunin

doi:10.2140/gt.2014.18.617

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Home > Journals > Geom. Topol. > Volume 18 > Issue 2 > Article

2014 Sweeping out sectional curvature

Dmitri Panov, Anton Petrunin

Geom. Topol. 18(2): 617-631 (2014). DOI: 10.2140/gt.2014.18.617

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Abstract

We observe that the maximal open set of constant curvature $κ$ in a Riemannian manifold of curvature $\geq κ$ or $\leq κ$ has a convexity-type property, which we call two-convexity. This statement is used to prove a number of rigidity statements in comparison geometry.