Uniqueness and nonuniqueness for Ricci flow on surfaces: Reverse cusp singularities

Details Uniqueness and nonuniqueness for Ricci flow on surfaces: Reverse cusp singularities Uniqueness and nonuniqueness for Ricci flow on surfaces: Reverse cusp singularities

2010-10-14

arxiv.org/abs/1010.2795v1

Mathematics

Differential Geometry

Scientific paper

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.

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