zbMATH — the first resource for mathematics

An energy approach to the problem of uniqueness for the Ricci flow. (English) Zbl 1303.53056
Author’s 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 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.

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
Full Text: DOI arXiv