Complete ancient solutions to the Ricci flow with pinched curvature

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Abstract

We show that any complete ancient solution to the Ricci flow equation with possibly unbounded curvature has constant curvature at each time if its curvature is pinched all the time. This is a slight extension of a result of Brendle, Huisken and Sinestrari for ancient solutions on compact manifolds. In our proof, we adapt their argument relying on the maximum principle with the help of Chen’s technique.

Original languageEnglish
Pages (from-to)485-506
Number of pages22
JournalCommunications in Analysis and Geometry
Volume25
Issue number2
DOIs
Publication statusPublished - 2017

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty

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