Translating Annuli for Mean Curvature Flow

Fuente: arXiv
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Autori principali: Hoffman, David, Martín, Francisco, White, Brian
Natura: Preprint
Pubblicazione: 2023
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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