The Cone Construction of Böhm and Wilking

Ben Andrews*, Christopher Hopper

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

In this section the remarkable formulas derived in the previous section, particularly the identities (12.13) and (12.14), will be applied to construct a family of cones preserved by the Ricci flow. We follow the argument presen- ted by Böhm and Wilking who applied it to produce a family of preserved cones interpolating between the cone of positive curvature operators and the line of constant positive curvature operators. The construction applies much more generally, so that given any preserved cone satisfying a few conditions, there is a family of cones linking that one to the ray of constant positive curvature operators. As we will see, this is a crucial step in proving that solutions the Ricci flow converge to spherical space forms.

Original languageEnglish
Title of host publicationThe Ricci Flow in Riemannian Geometry
Subtitle of host publicationA Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem
PublisherSpringer Verlag
Pages223-233
Number of pages11
ISBN (Print)9783642159664
DOIs
Publication statusPublished - 2011

Publication series

NameLecture Notes in Mathematics
Volume2011
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692

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