Generic mean curvature flow with obstacles
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911045607489536 |
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| author | Laux, Tim Takasao, Keisuke |
| author_facet | Laux, Tim Takasao, Keisuke |
| contents | We study the obstacle problem associated to mean curvature flow. We add to the geometric vanishing-viscosity approximation of Evans and Spruck a singular perturbation that penalizes the violation of the constraint, and pass to the limit. The resulting level set formulation has unique solutions - up to fattening. Extending the work of Evans and Spruck and a work by Ullrich and one of the authors, we show that generic level sets of this flow are distributional solutions of the obstacle problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06150 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generic mean curvature flow with obstacles Laux, Tim Takasao, Keisuke Analysis of PDEs Differential Geometry 53E10 (Primary), 35K65, 35A15, 35D30, 35D40 We study the obstacle problem associated to mean curvature flow. We add to the geometric vanishing-viscosity approximation of Evans and Spruck a singular perturbation that penalizes the violation of the constraint, and pass to the limit. The resulting level set formulation has unique solutions - up to fattening. Extending the work of Evans and Spruck and a work by Ullrich and one of the authors, we show that generic level sets of this flow are distributional solutions of the obstacle problem. |
| title | Generic mean curvature flow with obstacles |
| topic | Analysis of PDEs Differential Geometry 53E10 (Primary), 35K65, 35A15, 35D30, 35D40 |
| url | https://arxiv.org/abs/2507.06150 |