https://neckpinch.com/authors/daniel-ketover/New arXiv papers by Daniel Ketover, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2407.01240arxiv:2407.01240Mon, 01 Jul 2024 00:00:00 GMTDaniel Ketover — For each positive integer g we use variational methods to construct a genus g self-shrinker Σ_g in ℝ³ with entropy less than 2 and prismatic symmetry group D_(g+1)×ℤ₂. For g sufficiently large, the self-shrinker Σ_g has two graphical asymptotically conical ends and the sequence Σ_g converges on compact subsets to a plane with multiplicity two as g→∞. Angenent-Chopp-Ilmanen conjectured the existence of such self-shrinkers in 1995 based on numerical experiments. Using these surfaces as initial conditions for large g, we obtain examples of mean curvature flows in ℝ³ with smooth initial non-compact data that evolve non-uniquely after their first singular time.Mean curvature flowSelf-shrinkers & translatorsBoundaries & non-compactNumerics & visualization https://arxiv.org/abs/2310.05756arxiv:2310.05756Mon, 09 Oct 2023 00:00:00 GMTDaniel Ketover, Yevgeny Liokumovich — We give a new proof of the Smale conjecture for ℝP}³ and all lens spaces using minimal surfaces and min-max theory. For ℝP}³, the conjecture was first proved in 2019 by Bamler-Kleiner using Ricci flow.Ricci flowSmale conjecture & diffeomorphismsMinimal & CMC surfaces https://arxiv.org/abs/2307.01828arxiv:2307.01828Tue, 04 Jul 2023 00:00:00 GMTRobert Haslhofer, Daniel Ketover — In this paper, we prove that every strictly convex 3-ball with nonnegative Ricci-curvature contains at least 3 embedded free-boundary minimal 2-disks for any generic metric, and at least 2 solutions even without genericity assumption. Our approach combines ideas from mean curvature flow, min-max theory and degree theory. We also establish the existence of smooth free-boundary mean-convex foliations. In stark contrast to our prior work in the closed setting, the present result is sharp for generic metrics.Mean curvature flowFree boundary & capillaryMinimal & CMC surfaces