The Ricci flow on the sphere with marked points
Geometric Flows in Riemannian and Complex Geometry May 02, 2016 - May 06, 2016
Location: SLMath: Eisenbud Auditorium
Riemannian geometry
complex geometry
geometric analysis
geometric flow
Ricci flow
Ricci curvature
stability of solutions
singularities of flows
51D25 - Lattices of subspaces and geometric closure systems [See also 05B35]
51D30 - Continuous geometries, geometric closure systems and related topics [See also 06Cxx]
37A05 - Dynamical aspects of measure-preserving transformations
37Gxx - Local and nonlocal bifurcation theory for dynamical systems [See also 34C23, 34K18]
14503
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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14503
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