Volume preserving mean curvature flow of round surfaces in asymptotically flat spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909463942791168 |
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| author | Sinestrari, Carlo Tenan, Jacopo |
| author_facet | Sinestrari, Carlo Tenan, Jacopo |
| contents | We study the volume preserving mean curvature flow of a surface immersed in an asymptotically flat $3$-manifold modeling an isolated gravitating system in General Relativity. We show that, if the ambient manifold has positive ADM mass and the initial surface is round in a suitable sense, then the flow exists for all times and converges smoothly to a stable CMC surface. This extends to the asymptotically flat setting a classical result by Huisken-Yau (Invent. Math. 1996) and allows to construct a CMC foliation of the outer part of the manifold by an alternative approach to the ones by Nerz (Calc. Var. PDE, 2015) or by Eichmair-Koerber (J. Diff. Geometry, 2024). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13091 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Volume preserving mean curvature flow of round surfaces in asymptotically flat spaces Sinestrari, Carlo Tenan, Jacopo Differential Geometry Analysis of PDEs We study the volume preserving mean curvature flow of a surface immersed in an asymptotically flat $3$-manifold modeling an isolated gravitating system in General Relativity. We show that, if the ambient manifold has positive ADM mass and the initial surface is round in a suitable sense, then the flow exists for all times and converges smoothly to a stable CMC surface. This extends to the asymptotically flat setting a classical result by Huisken-Yau (Invent. Math. 1996) and allows to construct a CMC foliation of the outer part of the manifold by an alternative approach to the ones by Nerz (Calc. Var. PDE, 2015) or by Eichmair-Koerber (J. Diff. Geometry, 2024). |
| title | Volume preserving mean curvature flow of round surfaces in asymptotically flat spaces |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2501.13091 |