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.
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