Short-time persistence of bounded curvature under the Ricci flow

Brett Kotschwar

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arXiv · 1507.08246

Short-time persistence of bounded curvature under the Ricci flow

Brett Kotschwar

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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.

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Brett Kotschwar. 2015-07-29. Short-time persistence of bounded curvature under the Ricci flow. https://arxiv.org/abs/1507.08246

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