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

Brett Kotschwar

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arXiv · 1206.3225

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

Brett Kotschwar

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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 quantity and technique, we further prove a uniqueness theorem for subsolutions to a general class of mixed differential inequalities which implies an extension of Chen-Zhu's result to solutions (and initial data) of potentially unbounded curvature.

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Brett Kotschwar. 2012-06-14. An energy approach to the problem of uniqueness for the Ricci flow. https://arxiv.org/abs/1206.3225

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