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Young Women in Harmonic Analysis and PDE

December 2-4, 2016

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Franziska Monika Borer (ETH Zürich)

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

We show uniqueness of classical solutions of the normalised, two-dimensional Hamilton-Ricci flow on closed, smooth Riemannian surfaces for $H^2$ initial 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 nonuniqueness through reverse bubbling may occur.

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