An energy approach to the problem of uniqueness for the Ricci flow

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We revisit the problem of uniqueness for the Ricci flow and give a short, direct proof, based on the consideration of a simple energy quantity, of Hamilton/Chen-Zhu's theorem on the uniqueness of complete solutions of uniformly bounded curvature. With a variation of this technique, we prove a further uniqueness theorem for subsolutions to a general class of mixed differential inequalities and obtain an extension of Chen-Zhu's result to solutions (and initial data) of potentially unbounded curvature.

Original languageEnglish (US)
Pages (from-to)149-176
Number of pages28
JournalCommunications in Analysis and Geometry
Volume22
Issue number1
DOIs
StatePublished - 2014

Fingerprint

Ricci Flow
Uniqueness
Curvature
Subsolution
Differential Inequalities
Uniqueness Theorem
Energy
Theorem
Class

ASJC Scopus subject areas

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

Cite this

An energy approach to the problem of uniqueness for the Ricci flow. / Kotschwar, Brett.

In: Communications in Analysis and Geometry, Vol. 22, No. 1, 2014, p. 149-176.

Research output: Contribution to journalArticle

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