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Geometry-Topology Seminar

Thursday, December 5, 2019 - 4:30pm

Natasa Sesum

Rutgers University

Location

University of Pennsylvania

DRL 4C8

Perelman conjectured that the only $\kappa$-noncollapsed three dimensional ancient solutions to the Ricci flow are either the round cylinder, or the Bryant soliton, or the round sphere or the Perelman's solution. The last solution is not a soliton. Brendle solved the conjecture in a complete, noncompact case. In a joint work with Angenent, Brendle and Daskalopoulos we show that all closed noncollapsed ancient solutions have the unique precise asymptotics. Using that result, in a joint work with Brendle and Daskalopoulos we show Perelman's conjecture is true in a compact case as well.