## Geometry & Topology

### Sweeping out sectional curvature

#### Abstract

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.

#### Article information

Source
Geom. Topol., Volume 18, Number 2 (2014), 617-631.

Dates
Revised: 7 September 2013
Accepted: 28 September 2013
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732754

Digital Object Identifier
doi:10.2140/gt.2014.18.617

Mathematical Reviews number (MathSciNet)
MR3159972

Zentralblatt MATH identifier
1296.53091

Subjects
Primary: 53C24: Rigidity results

Keywords
rigidity comparison geometry

#### Citation

Panov, Dmitri; Petrunin, Anton. Sweeping out sectional curvature. Geom. Topol. 18 (2014), no. 2, 617--631. doi:10.2140/gt.2014.18.617. https://projecteuclid.org/euclid.gt/1513732754

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