On the long-time limit of the mean curvature flow in closed manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912731368521728 |
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| author | Mramor, Alexander Sun, Ao |
| author_facet | Mramor, Alexander Sun, Ao |
| contents | In this article we show that generally almost regular flows, introduced by Bamler and Kleiner, in closed 3-manifolds will either go extinct in finite time or flow to a collection of smooth embedded minimal surfaces, possibly with multiplicity. Using a perturbative argument then we construct piecewise almost regular flows which either go extinct in finite time or flow to a stable minimal surface, possibly with multiplicity. We apply these results to construct minimal surfaces in 3-manifolds in a variety of circumstances, mainly novel from the point of the view that the arguments are via parabolic methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03475 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the long-time limit of the mean curvature flow in closed manifolds Mramor, Alexander Sun, Ao Differential Geometry Analysis of PDEs Geometric Topology 53E10, 53A10 In this article we show that generally almost regular flows, introduced by Bamler and Kleiner, in closed 3-manifolds will either go extinct in finite time or flow to a collection of smooth embedded minimal surfaces, possibly with multiplicity. Using a perturbative argument then we construct piecewise almost regular flows which either go extinct in finite time or flow to a stable minimal surface, possibly with multiplicity. We apply these results to construct minimal surfaces in 3-manifolds in a variety of circumstances, mainly novel from the point of the view that the arguments are via parabolic methods. |
| title | On the long-time limit of the mean curvature flow in closed manifolds |
| topic | Differential Geometry Analysis of PDEs Geometric Topology 53E10, 53A10 |
| url | https://arxiv.org/abs/2412.03475 |