Sweeping out sectional curvature

Panov, Dmitri; Petrunin, Anton

doi:10.2140/gt.2014.18.617

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Sweeping out sectional curvature

Dmitri Panov and Anton Petrunin

Geometry & Topology 18 (2014) 617–631

DOI: 10.2140/gt.2014.18.617

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.

Keywords

rigidity, comparison geometry

Mathematical Subject Classification 2010

Primary: 53C24

Secondary: 53C20

References

Publication

Received: 29 March 2013

Revised: 7 September 2013

Accepted: 28 September 2013

Published: 30 January 2014

Proposed: Dmitri Burago

Seconded: John Lott, Simon Donaldson

Authors

Dmitri Panov
Department of Mathematics King’s College London London WC2R 2LS UK
http://www.kcl.ac.uk/nms/depts/mathematics/people/atoz/panovd.aspx
Anton Petrunin
Department of Mathematics Pennsylvania State University University Park, PA 16802 USA
http://www.math.psu.edu/petrunin/

Volume 18, issue 2 (2014)