The Ricci flow on the sphere with marked points
arXiv:1407.1118
Abstract
The Ricci flow on the 2-sphere with marked points is shown to converge in all three stable, semi-stable, and unstable cases. In the stable case, the flow was known to converge without any reparametrization, and a new proof of this fact is given. The semi-stable and unstable cases are new, and it is shown that the flow converges in the Gromov-Hausdorff topology to a limiting metric space which is also a 2-sphere, but with different marked points and hence a different complex structure. The limiting metric space carries a unique conical constant curvature metric in the semi-stable case, and a unique conical shrinking gradient Ricci soliton in the unstable case.
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- Ricci flow on surfaces with conic singularities
- Schauder estimates for equations with cone metrics, I
- Convergence of the conical Ricci flow on S2 to a soliton
- Stochastic Ricci Flow on Compact Surfaces
- New curvature flows in complex geometry
- A note on conical Kähler-Ricci flow on minimal elliptic Kähler surfaces
- Metric contraction of the cone divisor by the conical Kähler-Ricci flow
- On curvature pinching of conic 2-spheres
- Ricci measure for some singular Riemannian metrics