3 papers
math.DG2025
Infinite-dimensional dynamical instabilities of noncompact stationary Ricci flow solutions
Sigurd B. Angenent, Dan Knopf
Regarding Ricci flow as a dynamical system, we derive sufficient conditions for noncompact stationary (Ricci-flat) solutions to possess infinite-dimensional unstable manifolds, and…
math.DG2025
Local singularities of compact multiply warped Ricci flow solutions
James Isenberg, Dan Knopf, Zilu Ma +1
We demonstrate that any four-dimensional shrinking Ricci soliton , where is any two-dimensional complete noncompact surface and $…
math.DG2024
Asymptotic behavior of unstable perturbations of the Fubini-Study metric in Ricci flow
David Garfinkle, James Isenberg, Dan Knopf +1
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 indic…