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arXiv · 2605.09657

Expanders for Mean Curvature Flow and Counterexamples to Ilmanen's Genus-Reduction Conjecture

David Hoffman·Francisco Martin·Brian White
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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.

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David Hoffman, Francisco Martin, Brian White. 2026-05-10. Expanders for Mean Curvature Flow and Counterexamples to Ilmanen's Genus-Reduction Conjecture. https://arxiv.org/abs/2605.09657

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