Ricci Flow in Two Dimensions
Differential Geometry
2011-03-25 v1
Abstract
Ricci flow on two dimensional surfaces is far simpler than in the higher dimensional cases. This presents an opportunity to obtain much more detailed and comprehensive results. We review the basic facts about this flow, including the original results by Hamilton and Chow concerning Ricci flow on compact surfaces. The rationale for this paper, however, is especially to survey recent work concerning this flow on open surfaces, including various classes of both complete and incomplete surfaces, where a number of striking new phenomena have been observed.
Keywords
Cite
@article{arxiv.1103.4669,
title = {Ricci Flow in Two Dimensions},
author = {James Isenberg and Rafe Mazzeo and Natasa Sesum},
journal= {arXiv preprint arXiv:1103.4669},
year = {2011}
}
Comments
22 pages. To appear in the volume "Surveys in Geometric Analysis and Relativity celebrating Richard Schoen's 60th birthday."