A dimension descent scheme for the positive mass theorem in arbitrary dimension
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866914490929381376 |
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| author | Brendle, S. Wang, Y. |
| author_facet | Brendle, S. Wang, Y. |
| contents | We describe how the Schoen-Yau proof of the positive mass theorem can be extended to arbitrary dimensions. To overcome the problem of singularities, we propose a new inductive scheme. To carry out the inductive step, we use a combination of several techniques, including the shielding principle of Lesourd-Unger-Yau, as well as a conformal blow-up argument in the spirit of Bi-Hao-He-Shi-Zhu. Our arguments also rely on the Cheeger-Naber bound for the Minkowski dimension of the singular set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08473 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A dimension descent scheme for the positive mass theorem in arbitrary dimension Brendle, S. Wang, Y. Differential Geometry We describe how the Schoen-Yau proof of the positive mass theorem can be extended to arbitrary dimensions. To overcome the problem of singularities, we propose a new inductive scheme. To carry out the inductive step, we use a combination of several techniques, including the shielding principle of Lesourd-Unger-Yau, as well as a conformal blow-up argument in the spirit of Bi-Hao-He-Shi-Zhu. Our arguments also rely on the Cheeger-Naber bound for the Minkowski dimension of the singular set. |
| title | A dimension descent scheme for the positive mass theorem in arbitrary dimension |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2604.08473 |