Grim Raindrop: A Translating Solution to Curve Diffusion Flow
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910756372480000 |
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| author | Ogden, W. Jacob Warren, Micah |
| author_facet | Ogden, W. Jacob Warren, Micah |
| contents | We show the existence of a properly immersed translating solution to curve diffusion flow in the plane. Curve diffusion flow is a higher order version of curve shortening flow, namely \[ \left( \frac{dX}{dt}\right) ^{\perp}=-κ_{ss}N. \] |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15934 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Grim Raindrop: A Translating Solution to Curve Diffusion Flow Ogden, W. Jacob Warren, Micah Differential Geometry Analysis of PDEs 53E40 We show the existence of a properly immersed translating solution to curve diffusion flow in the plane. Curve diffusion flow is a higher order version of curve shortening flow, namely \[ \left( \frac{dX}{dt}\right) ^{\perp}=-κ_{ss}N. \] |
| title | Grim Raindrop: A Translating Solution to Curve Diffusion Flow |
| topic | Differential Geometry Analysis of PDEs 53E40 |
| url | https://arxiv.org/abs/2412.15934 |