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

2024/03/11 by David Garfinkle, James Isenberg, Garfinkle, David +5
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2403.06427

openalex publication_date 2024/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Kröncke has shown that the Fubini-Study metric is an unstable generalized stationary solution of Ricci flow [Krö20]. In this paper, we carry out numerical simulations which indicate that Ricci flow solutions originating at unstable perturbations of the Fubini-Study metric develop local singularities modeled by the blowdown soliton discovered in [FIK03].

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