Asymptotic behavior of unstable perturbations of the Fubini–Study metric in Ricci flow

Abstract: The Ricci flow can be regarded as a dynamical system on the space of Riemannian metrics. It is important to identify and study its fixed points, which are generalized Einstein metrics known as Ricci solitons. A prominent example of a Ricci soliton is the Fubini–Study metric on complex projective space. Kröncke has shown that the Fubini–Study metric is an unstable generalized stationary solution of Ricci flow. This raises an interesting question: What happens to Ricci flow solutions that start at arbitrarily small but unstable perturbations of the Fubini–Study metric? In a joint work with Garfinkle, Isenberg and Knopf, we carry out numerical simulations which indicate Ricci flow solutions originating at unstable perturbations of the Fubini–Study metric develop local singularities modeled by the FIK shrinking soliton discovered by Feldman, Ilmanen and Knopf.

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Mathematics

Audience: researchers in the topic

Comments: Meeting ID: 836 2536 5334 Password: 962501

IUT seminar in Geometry, Topology and PDE (IGTP)