Classification of Semigraphical Translators
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918392334647296 |
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| author | Martín, Francisco Sáez, Mariel Tsiamis, Raphael White, Brian |
| author_facet | Martín, Francisco Sáez, Mariel Tsiamis, Raphael White, Brian |
| contents | We complete the classification of semigraphical translators for mean curvature flow in $\mathbb{R}^3$ that was initiated by Hoffman-Martín-White. Specifically, we show that there is no solution to the translator equation on the upper half-plane with alternating positive and negative infinite boundary values, and we prove the uniqueness of pitchfork and helicoid translators. The proofs use Morse-Radó theory for translators and an angular maximum principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16889 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of Semigraphical Translators Martín, Francisco Sáez, Mariel Tsiamis, Raphael White, Brian Differential Geometry Analysis of PDEs Primary 53E10, 53C21, 53C42 We complete the classification of semigraphical translators for mean curvature flow in $\mathbb{R}^3$ that was initiated by Hoffman-Martín-White. Specifically, we show that there is no solution to the translator equation on the upper half-plane with alternating positive and negative infinite boundary values, and we prove the uniqueness of pitchfork and helicoid translators. The proofs use Morse-Radó theory for translators and an angular maximum principle. |
| title | Classification of Semigraphical Translators |
| topic | Differential Geometry Analysis of PDEs Primary 53E10, 53C21, 53C42 |
| url | https://arxiv.org/abs/2411.16889 |