A capillary problem for spacelike mean curvature flow in a cone of Minkowski space
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917142961586176 |
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| author | Klingenberg, Wilhelm Lambert, Ben Scheuer, Julian |
| author_facet | Klingenberg, Wilhelm Lambert, Ben Scheuer, Julian |
| contents | Consider a convex cone in three-dimensional Minkowski space which either contains the lightcone or is contained in it. This work considers mean curvature flow of a proper spacelike strictly mean convex disc in the cone which is graphical with respect to its rays. Its boundary is required to have constant intersection angle with the boundary of the cone. We prove that the corresponding parabolic boundary value problem for the graph admits a solution for all time which rescales to a self-similarly expanding solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02414 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A capillary problem for spacelike mean curvature flow in a cone of Minkowski space Klingenberg, Wilhelm Lambert, Ben Scheuer, Julian Differential Geometry Analysis of PDEs Consider a convex cone in three-dimensional Minkowski space which either contains the lightcone or is contained in it. This work considers mean curvature flow of a proper spacelike strictly mean convex disc in the cone which is graphical with respect to its rays. Its boundary is required to have constant intersection angle with the boundary of the cone. We prove that the corresponding parabolic boundary value problem for the graph admits a solution for all time which rescales to a self-similarly expanding solution. |
| title | A capillary problem for spacelike mean curvature flow in a cone of Minkowski space |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2304.02414 |