Ancient solutions and translators of Lagrangian mean curvature flow
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916097154875392 |
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| author | Lotay, Jason D. Schulze, Felix Székelyhidi, Gábor |
| author_facet | Lotay, Jason D. Schulze, Felix Székelyhidi, Gábor |
| contents | Suppose that $\mathcal{M}$ is an almost calibrated, exact, ancient solution of Lagrangian mean curvature flow in $\mathbb{C}^n$. We show that if $\mathcal{M}$ has a blow-down given by the static union of two Lagrangian subspaces with distinct Lagrangian angles that intersect along a line, then $\mathcal{M}$ is a translator. In particular in $\mathbb{C}^2$, all almost calibrated, exact, ancient solutions of Lagrangian mean curvature flow with entropy less than 3 are special Lagrangian, a union of planes, or translators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_13836 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Ancient solutions and translators of Lagrangian mean curvature flow Lotay, Jason D. Schulze, Felix Székelyhidi, Gábor Differential Geometry 53E10 Suppose that $\mathcal{M}$ is an almost calibrated, exact, ancient solution of Lagrangian mean curvature flow in $\mathbb{C}^n$. We show that if $\mathcal{M}$ has a blow-down given by the static union of two Lagrangian subspaces with distinct Lagrangian angles that intersect along a line, then $\mathcal{M}$ is a translator. In particular in $\mathbb{C}^2$, all almost calibrated, exact, ancient solutions of Lagrangian mean curvature flow with entropy less than 3 are special Lagrangian, a union of planes, or translators. |
| title | Ancient solutions and translators of Lagrangian mean curvature flow |
| topic | Differential Geometry 53E10 |
| url | https://arxiv.org/abs/2204.13836 |