Sweeping out sectional curvature

Dmitri Panov, Anton Petrunin

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We observe that the maximal open set of constant curvature
κ in a Riemannian manifold of curvature ≥ κ or ≤ 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.
Original languageEnglish
Pages (from-to)617-631
JournalGeometry & Topology
Issue number2
Publication statusPublished - 30 Jan 2014


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  • Sweeping out sectional curvature

    Panov, D. & Petrunin, A., 19 Jun 2011.

    Research output: Working paper/PreprintPreprint


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