Uniqueness of Semigraphical Translators

We prove a conjecture by Hoffman, White, and the first author regarding the uniqueness of pitchfork and helicoid translators of the mean curvature flow in \(\mathbb{R}^3\). We employ an arc-counting argument motivated by Morse-Radó theory for translators and a rotational maximum principle. Applicati...

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Bibliographic Details
Published in:arXiv.org 2024-11
Main Authors: Martín, Francisco, Sáez, Mariel, Tsiamis, Raphael
Format: Article
Language:English
Subjects:
Maximum principle
Translators
Uniqueness
Online Access:Get full text
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Summary:We prove a conjecture by Hoffman, White, and the first author regarding the uniqueness of pitchfork and helicoid translators of the mean curvature flow in \(\mathbb{R}^3\). We employ an arc-counting argument motivated by Morse-Radó theory for translators and a rotational maximum principle. Applications to the classification of semigraphical translators in \(\mathbb{R}^3\) and their limits are discussed, strengthening compactness results of the first author with Hoffman-White and with Gama-Moller.
ISSN:2331-8422