https://neckpinch.com/authors/tom-ilmanen/New arXiv papers by Tom Ilmanen, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2601.21952arxiv:2601.21952Thu, 29 Jan 2026 00:00:00 GMTTom Ilmanen — The aim in these lectures is to study singularity formation, nonuniqueness, and topological change in motion by mean curvature.Mean curvature flowSingularities https://arxiv.org/abs/2601.21133arxiv:2601.21133Thu, 29 Jan 2026 00:00:00 GMTTom Ilmanen — This paper proves that, at the first singular time for a smoothly immersed surface moving by mean curvature flow in a n-manifold, each tangent flow is given by a smooth, branched shrinker, possibly with multiplicity. If n=3 and if the initial surface is embedded, then the shrinker is smoothly embedded without branch points, but possibly with multiplicity. A key ingredient of the proof is a new, local version of the Gauss-Bonnet formula.Mean curvature flowRicci solitonsSingularities https://arxiv.org/abs/2406.18703arxiv:2406.18703Wed, 26 Jun 2024 00:00:00 GMTTom Ilmanen, Brian White — For each g≥ 3, we prove existence of a compact, connected, smoothly embedded, genus-g surface M_g with the following property: under mean curvature flow, there is exactly one singular point at the first singular time, and the tangent flow at the singularity is given by a shrinker with genus (g-1) and with two ends. Furthermore, we show that if g is sufficiently large, then M_g fattens at the first singular time. As g→∞, the shrinker converges to a multiplicity 2 plane.Mean curvature flowRicci solitonsSingularities