Expanders for Mean Curvature Flow and Counterexamples to Ilmanen's Genus-Reduction Conjecture
Differential Geometry
2026-05-12 v1
Abstract
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.
Cite
@article{arxiv.2605.09657,
title = {Expanders for Mean Curvature Flow and Counterexamples to Ilmanen's Genus-Reduction Conjecture},
author = {David Hoffman and Francisco Martin and Brian White},
journal= {arXiv preprint arXiv:2605.09657},
year = {2026}
}
Comments
43 pages, 1 figure