16 citations · 83 across the 23 of their papers we have counts for
26 papers
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…
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 $…
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 indicat…
A numerical stability analysis of mean curvature flow of noncompact hypersurfaces with Type-II curvature blowup: II
David Garfinkle, James Isenberg, Dan Knopf +1
In previous work [GIKW21], we have presented evidence from numerical simulations that the Type-II singularities of mean curvature flow (MCF) of rotationally-symmetric, complete, no…
A numerical stability analysis of mean curvature flow of noncompact hypersurfaces with Type-II curvature blowup
David Garfinkle, James Isenberg, Dan Knopf +1
We present a numerical study of the local stability of mean curvature flow of rotationally symmetric, complete noncompact hypersurfaces with Type-II curvature blowup. Our numerical…
Singularity formation of complete Ricci flow solutions
Timothy Carson, James Isenberg, Dan Knopf +1
We study singularity formation of complete Ricci flow solutions, motivated by two applications: (a) improving the understanding of the behavior of the essential blowup sequences of…