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arXiv · 2507.19428

Self-expanders of positive genus

Guanhua Shao·Jiahua Zou
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Abstract

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.

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Guanhua Shao, Jiahua Zou. 2025-07-25. Self-expanders of positive genus. https://arxiv.org/abs/2507.19428

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