Ricci Flow in Two Dimensions
arXiv:1103.4669
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.
22 pages. To appear in the volume "Surveys in Geometric Analysis and Relativity celebrating Richard Schoen's 60th birthday."
References in corpus (1)
Cited by in corpus (6)
- Ricci flow on surfaces with conic singularities
- Bessel Functions, Heat Kernel and the Conical Kähler-Ricci Flow
- The Yamabe flow on incomplete manifolds
- On the properties of the combinatorial Ricci flow for surfaces
- Yamabe flow on manifolds with edges
- Uniformization of compact foliated spaces by surfaces of hyperbolic type