Uniqueness of Weak Solutions for the Normalised Ricci Flow in Two Dimensions
Analysis of PDEs
2016-01-27 v1 Differential Geometry
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 -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.
Keywords
Cite
@article{arxiv.1601.06853,
title = {Uniqueness of Weak Solutions for the Normalised Ricci Flow in Two Dimensions},
author = {Franziska Borer},
journal= {arXiv preprint arXiv:1601.06853},
year = {2016}
}