Geometry & Topology

Sweeping out sectional curvature

Dmitri Panov and Anton Petrunin

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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

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

Received: 29 March 2013
Revised: 7 September 2013
Accepted: 28 September 2013
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C24: Rigidity results
Secondary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]

rigidity comparison geometry


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

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