The Ricci flow on the sphere with marked points
Location: MSRI: Simons Auditorium
stability of solutions
singularities of flows
We study the limiting behavior of the Ricci flow on the 2-sphere with marked points. We show that the normalized Ricci flow will always converge to a unique constant curvature metric or a shrinking gradient soliton metric. In the semi-stable and unstable cases of the 2-sphere with more than two marked points, the limiting metric space carries a different conical and the complex structure from the initial structure. We also study the blow-up behavior of the flow in the semi-stable and unstable cases. This is a joint work with Phong, Sturm and Wang
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