Translating Annuli for Mean Curvature Flow
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917737713893376 |
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| author | Hoffman, David Martín, Francisco White, Brian |
| author_facet | Hoffman, David Martín, Francisco White, Brian |
| contents | We construct a family of complete, properly embedded, annular translators $M$ such that $M$ lies in a slab and is invariant under reflections in the vertical coordinate planes. Each translator in the family is asymptotic as $z\to -\infty$ to four vertical planes $\{y= \pm b\}$ and $\{y= \pm B\}$, where $0<b \le B < \infty$. We call $b$ and $B$ the inner width and the (outer) width of the translator. We show that for each $b \ge π/2$ and each $s>0$, there is a translator in the family with inner width $b$ and with necksize $s$. (We also show that there are no translators with inner width $<π/2$ having the properties of the examples we construct.) |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_02210 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Translating Annuli for Mean Curvature Flow Hoffman, David Martín, Francisco White, Brian Differential Geometry Analysis of PDEs 53C44, 53C21, 53C42 We construct a family of complete, properly embedded, annular translators $M$ such that $M$ lies in a slab and is invariant under reflections in the vertical coordinate planes. Each translator in the family is asymptotic as $z\to -\infty$ to four vertical planes $\{y= \pm b\}$ and $\{y= \pm B\}$, where $0<b \le B < \infty$. We call $b$ and $B$ the inner width and the (outer) width of the translator. We show that for each $b \ge π/2$ and each $s>0$, there is a translator in the family with inner width $b$ and with necksize $s$. (We also show that there are no translators with inner width $<π/2$ having the properties of the examples we construct.) |
| title | Translating Annuli for Mean Curvature Flow |
| topic | Differential Geometry Analysis of PDEs 53C44, 53C21, 53C42 |
| url | https://arxiv.org/abs/2308.02210 |