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Sweeping out sectional curvature

Research output: Working paper/PreprintPreprint

D. Panov, A. Petrunin

Original languageEnglish
Published19 Jun 2011

Bibliographical note

11 pages

Documents

  • pdf

    1106.3736v4, 191 KB, application/pdf

    Uploaded date:21 Jul 2015

    Version:Submitted manuscript

    Preprint in ArXiv

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King's Authors

Abstract

We observe that the maximal open set of constant curvature k in a Riemannian manifold with curvature bounded below or above by k has a convexity type property, which we call "two-convexity". This statement is used to prove a number of rigidity statements in comparison geometry.

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