A local curvature estimate for the Ricci flow

Brett Kotschwar, Ovidiu Munteanu, Jiaping Wang

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We show that the norm of the Riemann curvature tensor of any smooth solution to the Ricci flow can be explicitly estimated in terms of its initial values on a given ball, a local uniform bound on the Ricci tensor, and the elapsed time. This provides a new, direct proof of a result of Šesǔm, which asserts that the curvature of a solution on a compact manifold cannot blow up while the Ricci curvature remains bounded, and extends its conclusions to the noncompact setting. We also prove that the Ricci curvature must blow up at least linearly along a subsequence at a finite time singularity.

Original languageEnglish (US)
Pages (from-to)2604-2630
Number of pages27
JournalJournal of Functional Analysis
Volume271
Issue number9
DOIs
StatePublished - Nov 1 2016

Fingerprint

Ricci Flow
Ricci Curvature
Blow-up
Curvature
Finite-time Singularities
Ricci Tensor
Uniform Bound
Curvature Tensor
Smooth Solution
Subsequence
Compact Manifold
Estimate
Ball
Linearly
Norm

Keywords

  • Curvature bound
  • Ricci flow

ASJC Scopus subject areas

  • Analysis

Cite this

A local curvature estimate for the Ricci flow. / Kotschwar, Brett; Munteanu, Ovidiu; Wang, Jiaping.

In: Journal of Functional Analysis, Vol. 271, No. 9, 01.11.2016, p. 2604-2630.

Research output: Contribution to journalArticle

Kotschwar, Brett ; Munteanu, Ovidiu ; Wang, Jiaping. / A local curvature estimate for the Ricci flow. In: Journal of Functional Analysis. 2016 ; Vol. 271, No. 9. pp. 2604-2630.
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