Sweeping out sectional curvature

Dmitri Panov, Anton Petrunin

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We observe that the maximal open set of constant curvature κ in a Riemannian manifold of curvature ≥ κ or 6 ≤ 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 (US)
Pages (from-to)617-631
Number of pages15
JournalGeometry and Topology
Issue number2
StatePublished - Jan 30 2014

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


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