Sweeping out sectional curvature

Dmitri Panov; Anton Petrunin

doi:10.2140/gt.2014.18.617

Sweeping out sectional curvature

Dmitri Panov, Anton Petrunin

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	617-631
Number of pages	15
Journal	Geometry and Topology
Volume	18
Issue number	2
DOIs	https://doi.org/10.2140/gt.2014.18.617
State	Published - Jan 30 2014

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.2140/gt.2014.18.617

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title = "Sweeping out sectional curvature",

abstract = "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.",

author = "Dmitri Panov and Anton Petrunin",

year = "2014",

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Sweeping out sectional curvature

Abstract

All Science Journal Classification (ASJC) codes

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