학술논문
Translating Annuli for Mean Curvature Flow
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Working Paper
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Abstract
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 $00$, 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 $<\pi/2$ having the properties of the examples we construct.)
Comment: 83 pages, 9 figures. Revised version (Aug 26, 2023) includes a slightly expanded introduction, and additional citations
Comment: 83 pages, 9 figures. Revised version (Aug 26, 2023) includes a slightly expanded introduction, and additional citations