Self-expanders of positive genus
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916884708851712 |
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| author | Shao, Guanhua Zou, Jiahua |
| author_facet | Shao, Guanhua Zou, Jiahua |
| contents | For a general class of cones in $\mathbb{R}^3$, we construct self-expanders of positive genus asymptotic to these cones. As a result, we use these self-expanders to construct a mean curvature flow with genus strictly decreasing but not to zero at the first singular time. We also construct a sequence of self-expanders with unbounded genus which are asymptotic to the same rotationally symmetric cone. Moreover, we characterize the asymptotic behavior of the sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19428 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-expanders of positive genus Shao, Guanhua Zou, Jiahua Differential Geometry 53A10 (Primary), 53E10 (Secondary) For a general class of cones in $\mathbb{R}^3$, we construct self-expanders of positive genus asymptotic to these cones. As a result, we use these self-expanders to construct a mean curvature flow with genus strictly decreasing but not to zero at the first singular time. We also construct a sequence of self-expanders with unbounded genus which are asymptotic to the same rotationally symmetric cone. Moreover, we characterize the asymptotic behavior of the sequence. |
| title | Self-expanders of positive genus |
| topic | Differential Geometry 53A10 (Primary), 53E10 (Secondary) |
| url | https://arxiv.org/abs/2507.19428 |