https://neckpinch.com/authors/haotian-wu/New arXiv papers by Haotian Wu, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2403.06427arxiv:2403.06427Mon, 11 Mar 2024 00:00:00 GMTDavid Garfinkle, James Isenberg, Dan Knopf, Haotian Wu — 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].Ricci flowSingularitiesStability & uniquenessNumerics & visualization https://arxiv.org/abs/2210.10296arxiv:2210.10296Wed, 19 Oct 2022 00:00:00 GMTHaotian Wu, Zhou Zhang — We improve the understanding of both finite time and infinite time singularities of the modified Kähler-Ricci flow as initiated by the second author of this paper in [26]. This is done by relating the modified Kähler-Ricci flow with the recent studies on the classic Kähler-Ricci flow and the degenerate complex Monge-Ampère equation.Ricci flowKähler–Ricci flowSingularitiesKähler geometry https://arxiv.org/abs/2206.01890arxiv:2206.01890Sat, 04 Jun 2022 00:00:00 GMTDavid Garfinkle, James Isenberg, Dan Knopf, Haotian Wu — 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, noncompact embedded hypersurfaces constructed in [IW19, IWZ21] are stable. More precisely, it is shown in that paper that for small rotationally-symmetric perturbations of initial embeddings near the "tip", numerical simulations of MCF of such initial embeddings develop the same Type-II singularities with the same "bowl soliton" blowup behaviors in a neighborhood of the singularity. It is also shown in that work that for small rotationally-symmetric perturbations of the initial embeddings that are sufficiently far away from the tip, MCF develops Type-I "neckpinch" singularities. In this work, we again use numerical simulations to show that MCF subject to initial perturbations that are not rotationally symmetric behaves asymptotically like it does for rotationally-symmetric perturbations. In particular, if we impose sinusoidal angular dependence on the initial embeddings, we find that for perturbations near the tip, evolutions by MCF asymptotically lose their angular dependence – becoming round – and develop Type-II bowl soliton singularities. As well, if we impose sinusoidal angular dependence on the initial embeddings for perturbations sufficiently far from the tip, the angular dependence again disappears as Type-I neckpinch singularities develop. The numerical analysis carried out in this work is an adaptation of the "overlap" method introduced in [GIKW21] and permits angular dependence.Mean curvature flowSelf-shrinkers & translatorsSingularitiesStability & uniquenessBoundaries & non-compactRotational symmetry & warped productsNumerics & visualization