Uniqueness and nonuniqueness for Ricci flow on surfaces: Reverse cusp singularities
Differential Geometry
2010-10-15 v1 Analysis of PDEs
Abstract
We extend the notion of what it means for a complete Ricci flow to have a given initial metric, and consider the resulting well-posedness issues that arise in the 2D case. On one hand we construct examples of nonuniqueness by showing that surfaces with cusps can evolve either by keeping the cusps or by contracting them. On the other hand, by adding a noncollapsedness assumption for the initial metric, we establish a uniqueness result.
Keywords
Cite
@article{arxiv.1010.2795,
title = {Uniqueness and nonuniqueness for Ricci flow on surfaces: Reverse cusp singularities},
author = {Peter Topping},
journal= {arXiv preprint arXiv:1010.2795},
year = {2010}
}