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arXiv · 1601.06853

Uniqueness of Weak Solutions for the Normalised Ricci Flow in Two Dimensions

Franziska Borer
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Abstract

We show uniqueness of classical solutions of the normalised two-dimensional Hamilton-Ricci flow on closed, smooth manifolds for smooth data among solutions satisfying (essentially) only a uniform bound for the Liouville energy and a natural space-time $L^2$-bound for the time derivative of the solution. The result is surprising when compared with results for the harmonic map heat flow, where non-uniqueness through reverse bubbling may occur.

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Franziska Borer. 2016-01-26. Uniqueness of Weak Solutions for the Normalised Ricci Flow in Two Dimensions. https://arxiv.org/abs/1601.06853

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