Genus one singularities in mean curvature flow
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908688276520960 |
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| author | Chu, Adrian Chun-Pong Sun, Ao |
| author_facet | Chu, Adrian Chun-Pong Sun, Ao |
| contents | We show that for certain one-parameter families of initial conditions in $\mathbb R^3$, when we run mean curvature flow, a genus one singularity must appear in one of the flows. Moreover, such a singularity is robust under perturbation of the family of initial conditions. This contrasts sharply with the case of just a single flow. As an application, we construct an embedded, genus one self-shrinker with entropy lower than a shrinking doughnut. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05923 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Genus one singularities in mean curvature flow Chu, Adrian Chun-Pong Sun, Ao Differential Geometry Analysis of PDEs Geometric Topology We show that for certain one-parameter families of initial conditions in $\mathbb R^3$, when we run mean curvature flow, a genus one singularity must appear in one of the flows. Moreover, such a singularity is robust under perturbation of the family of initial conditions. This contrasts sharply with the case of just a single flow. As an application, we construct an embedded, genus one self-shrinker with entropy lower than a shrinking doughnut. |
| title | Genus one singularities in mean curvature flow |
| topic | Differential Geometry Analysis of PDEs Geometric Topology |
| url | https://arxiv.org/abs/2308.05923 |