https://neckpinch.com/authors/david-hoffman/New arXiv papers by David Hoffman, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2605.09657arxiv:2605.09657Sun, 10 May 2026 00:00:00 GMTDavid Hoffman, Francisco Martin, Brian White — We construct new expanders for mean curvature flow that are smoothly asymptotic to cones arising from certain shrinkers. For each such cone, we prove the existence of expanders of arbitrarily large genus. Thus, for a fixed incoming shrinker, the genus of the outgoing expander can be chosen much larger than the genus before the singularity, contrary to Ilmanen's genus-reduction conjecture.Mean curvature flowRicci solitonsSingularities https://arxiv.org/abs/2502.20340arxiv:2502.20340Thu, 27 Feb 2025 00:00:00 GMTDavid Hoffman, Francisco Martin, Brian White — We prove existence for many examples of shrinkers by producing compact, smoothly embedded surfaces that, under mean curvature flow, develop singularities at which the shrinkers occur as blowups.Mean curvature flowRicci solitonsSingularities https://arxiv.org/abs/2308.02210arxiv:2308.02210Fri, 04 Aug 2023 00:00:00 GMTDavid Hoffman, Francisco Martín, Brian White — We construct a family of complete, properly embedded, annular translators M such that M lies in a slab and is invariant under reflections in the vertical coordinate planes. Each translator in the family is asymptotic as z→ -∞ to four vertical planes y= ± b\ and y= ± B\, where 0<b ≤ B < ∞. We call b and B the inner width and the (outer) width of the translator. We show that for each b ≥ π/2 and each s>0, there is a translator in the family with inner width b and with necksize s. (We also show that there are no translators with inner width <π/2 having the properties of the examples we construct.)Mean curvature flowSelf-shrinkers & translators https://arxiv.org/abs/2304.11447arxiv:2304.11447Sat, 22 Apr 2023 00:00:00 GMTD. Hoffman, F. Martin, B. White — In this paper, we describe new annular examples of complete translating solitons for the mean curvature flow and how they are related to a family of translating graphs, the Δ-wings. In addition, we will prove several related results that answer questions that arise naturally in this investigation. These results apply to translators in general, not just to graphs or annuli.Mean curvature flowSelf-shrinkers & translators