ADM mass for $C^0$ metrics and distortion under Ricci-DeTurck flow
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866912250970767360 |
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| author | Burkhardt-Guim, Paula |
| author_facet | Burkhardt-Guim, Paula |
| contents | We show that there exists a quantity, depending only on $C^0$ data of a Riemannian metric, that agrees with the usual ADM mass at infinity whenever the ADM mass exists, but has a well-defined limit at infinity for any continuous Riemannian metric that is asymptotically flat in the $C^0$ sense and has nonnegative scalar curvature in the sense of Ricci flow. Moreover, the $C^0$ mass at infinity is independent of choice of $C^0$-asymptotically flat coordinate chart, and the $C^0$ local mass has controlled distortion under Ricci-DeTurck flow when coupled with a suitably evolving test function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_14550 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | ADM mass for $C^0$ metrics and distortion under Ricci-DeTurck flow Burkhardt-Guim, Paula Differential Geometry We show that there exists a quantity, depending only on $C^0$ data of a Riemannian metric, that agrees with the usual ADM mass at infinity whenever the ADM mass exists, but has a well-defined limit at infinity for any continuous Riemannian metric that is asymptotically flat in the $C^0$ sense and has nonnegative scalar curvature in the sense of Ricci flow. Moreover, the $C^0$ mass at infinity is independent of choice of $C^0$-asymptotically flat coordinate chart, and the $C^0$ local mass has controlled distortion under Ricci-DeTurck flow when coupled with a suitably evolving test function. |
| title | ADM mass for $C^0$ metrics and distortion under Ricci-DeTurck flow |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2208.14550 |