Volume preserving spacetime mean curvature flow and foliations of initial data sets
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916755740295168 |
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| author | Tenan, Jacopo |
| author_facet | Tenan, Jacopo |
| contents | We consider a volume preserving curvature evolution of surfaces in an asymptotically Euclidean initial data set with positive ADM-energy. The speed is given by a nonlinear function of the mean curvature which generalizes the spacetime mean curvature recently considered by Cederbaum-Sakovich (Calc. Var. PDE, 2021). Following a classical approach by Huisken-Yau (Invent. Math., 1996), we show that the flow starting from suitably round initial surfaces exists for all times and converges to a constant (spacetime) curvature limit. This provides an alternative construction of the CSTMC foliation by Cederbaum-Sakovich and has applications in the definition of center of mass of an isolated system in General Relativity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12971 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Volume preserving spacetime mean curvature flow and foliations of initial data sets Tenan, Jacopo Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs We consider a volume preserving curvature evolution of surfaces in an asymptotically Euclidean initial data set with positive ADM-energy. The speed is given by a nonlinear function of the mean curvature which generalizes the spacetime mean curvature recently considered by Cederbaum-Sakovich (Calc. Var. PDE, 2021). Following a classical approach by Huisken-Yau (Invent. Math., 1996), we show that the flow starting from suitably round initial surfaces exists for all times and converges to a constant (spacetime) curvature limit. This provides an alternative construction of the CSTMC foliation by Cederbaum-Sakovich and has applications in the definition of center of mass of an isolated system in General Relativity. |
| title | Volume preserving spacetime mean curvature flow and foliations of initial data sets |
| topic | Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2407.12971 |