Short-time persistence of bounded curvature under the Ricci flow

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Abstract

We use a first-order energy quantity to prove a strengthened statement of uniqueness for the Ricci flow. One consequence of this statement is that if a complete solution on a noncompact manifold has uniformly bounded Ricci curvature, then its sectional curvature will remain bounded for a short time if it is bounded initially. In other words, the Weyl curvature tensor of a complete solution to the Ricci flow cannot become unbounded instantaneously if the Ricci curvature remains bounded.

Original languageEnglish (US)
Pages (from-to)427-447
Number of pages21
JournalMathematical Research Letters
Volume24
Issue number2
Publication statusPublished - 2017

ASJC Scopus subject areas

  • Mathematics(all)

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