Expanders for Mean Curvature Flow and Counterexamples to Ilmanen's Genus-Reduction Conjecture
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918493721460736 |
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| author | Hoffman, David Martin, Francisco White, Brian |
| author_facet | Hoffman, David Martin, Francisco White, Brian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09657 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Expanders for Mean Curvature Flow and Counterexamples to Ilmanen's Genus-Reduction Conjecture Hoffman, David Martin, Francisco White, Brian Differential Geometry 53C44 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. |
| title | Expanders for Mean Curvature Flow and Counterexamples to Ilmanen's Genus-Reduction Conjecture |
| topic | Differential Geometry 53C44 |
| url | https://arxiv.org/abs/2605.09657 |