$X$-ADM Mass and $X$-Positive Mass Theorem
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910019862134784 |
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| author | Mantegazza, Carlo Oronzio, Francesca |
| author_facet | Mantegazza, Carlo Oronzio, Francesca |
| contents | For a given admissible vector field $X$, we define a geometric quantity for asymptotically flat $3$--manifolds, called $X$--ADM mass and we establish a relative positive mass theorem via a monotonicity formula along the level sets of a suitable Green's function. Under different assumptions on $X$, we obtain generalizations of the ``classical'' positive mass theorem, like the one for weighted manifolds and the one ``with charge'' under some topological restrictions. Finally, we also discuss the rigidity cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11372 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $X$-ADM Mass and $X$-Positive Mass Theorem Mantegazza, Carlo Oronzio, Francesca Differential Geometry For a given admissible vector field $X$, we define a geometric quantity for asymptotically flat $3$--manifolds, called $X$--ADM mass and we establish a relative positive mass theorem via a monotonicity formula along the level sets of a suitable Green's function. Under different assumptions on $X$, we obtain generalizations of the ``classical'' positive mass theorem, like the one for weighted manifolds and the one ``with charge'' under some topological restrictions. Finally, we also discuss the rigidity cases. |
| title | $X$-ADM Mass and $X$-Positive Mass Theorem |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2602.11372 |