Communications in Analysis and Geometry

Volume 22 (2014)

Number 1

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

Pages: 149 – 176

DOI: http://dx.doi.org/10.4310/CAG.2014.v22.n1.a3

Author

Brett Kotschwar (Arizona State University, Tempe, Ariz., U.S.A.)

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.

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