English

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 L2L^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.

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}
}