Existence proofs for rotationally symmetric translating solutions to mean curvature flow
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916752339763200 |
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| author | Raji, Hakar Schnürer, Oliver C. |
| author_facet | Raji, Hakar Schnürer, Oliver C. |
| contents | There exist rotationally symmetric translating solutions to mean curvature flow that can be written as a graph over Euclidean space. This result is well-known. Its proof uses the symmetry and techniques from partial differential equations. However, the result can also be formulated as an existence result for a singular ordinary differential equation. Here, we provide different methods to prove existence of these solutions based on the study of the singular ordinary differential equation without using methods from partial differential equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_16688 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence proofs for rotationally symmetric translating solutions to mean curvature flow Raji, Hakar Schnürer, Oliver C. Differential Geometry 53E10, 34A12 There exist rotationally symmetric translating solutions to mean curvature flow that can be written as a graph over Euclidean space. This result is well-known. Its proof uses the symmetry and techniques from partial differential equations. However, the result can also be formulated as an existence result for a singular ordinary differential equation. Here, we provide different methods to prove existence of these solutions based on the study of the singular ordinary differential equation without using methods from partial differential equations. |
| title | Existence proofs for rotationally symmetric translating solutions to mean curvature flow |
| topic | Differential Geometry 53E10, 34A12 |
| url | https://arxiv.org/abs/2505.16688 |