Asymptotic rigidity of noncompact shrinking gradient Ricci solitons
Geometric Flows in Riemannian and Complex Geometry May 02, 2016 - May 06, 2016
Location: SLMath: Eisenbud Auditorium
complex geometry
Riemannian geometry
geometric analysis
geometric flow
Ricci flow
soliton solutions
asymptotic behavior of solutions
positive curvature
classification of solutions
51D25 - Lattices of subspaces and geometric closure systems [See also 05B35]
51D30 - Continuous geometries, geometric closure systems and related topics [See also 06Cxx]
35P20 - Asymptotic distributions of eigenvalues in context of PDEs
35Q51 - Soliton equations {For dynamical systems and ergodic theory, see 37K40}
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Shrinking gradient Ricci solitons are models for the local geometry about a developing singularity under the
Ricci flow. At present, all known examples of complete noncompact shrinkers are either locally reducible as products
or possess conical structures at infinity. I will survey some recent results related to the problem of their classification
including some joint work with Lu Wang in which we study the uniqueness of such asymptotic structures as a problem of parabolic unique continuation
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