Rigidity and non-existence results for collapsed translators
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914333313728512 |
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| author | Impera, Debora Møller, Niels Martin Rimoldi, Michele |
| author_facet | Impera, Debora Møller, Niels Martin Rimoldi, Michele |
| contents | We prove a rigidity result for mean curvature self-translating solitons, characterizing the grim reaper cylinder as the only finite entropy self-translating 2-surface in $\mathbb{R}^3$ of width $π$ and bounded from below. The proof makes use of parabolicity in a weighted setting applied to a suitable universally $L$-superharmonic function defined on translaters in such slabs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_11953 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rigidity and non-existence results for collapsed translators Impera, Debora Møller, Niels Martin Rimoldi, Michele Differential Geometry Analysis of PDEs 53A10, 53E10 (49Q05, 53C42) We prove a rigidity result for mean curvature self-translating solitons, characterizing the grim reaper cylinder as the only finite entropy self-translating 2-surface in $\mathbb{R}^3$ of width $π$ and bounded from below. The proof makes use of parabolicity in a weighted setting applied to a suitable universally $L$-superharmonic function defined on translaters in such slabs. |
| title | Rigidity and non-existence results for collapsed translators |
| topic | Differential Geometry Analysis of PDEs 53A10, 53E10 (49Q05, 53C42) |
| url | https://arxiv.org/abs/2304.11953 |