A proof for the Riemannian positive mass theorem up to dimension 19
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911547169701888 |
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| author | Bi, Yuchen Hao, Tianze He, Shihang Shi, Yuguang Zhu, Jintian |
| author_facet | Bi, Yuchen Hao, Tianze He, Shihang Shi, Yuguang Zhu, Jintian |
| contents | In this paper, we prove the Riemannian positive mass theorem up to dimension $19$, building on a combination of torical symmetrization and the singularity blow-up technique developed in [HSY26], together with the generic regularity theory for area-minimizing hypersurfaces established in [CMS23, CMSW25]. Similar ideas are also employed to investigate the Geroch conjecture up to dimension $12$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02769 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A proof for the Riemannian positive mass theorem up to dimension 19 Bi, Yuchen Hao, Tianze He, Shihang Shi, Yuguang Zhu, Jintian Differential Geometry In this paper, we prove the Riemannian positive mass theorem up to dimension $19$, building on a combination of torical symmetrization and the singularity blow-up technique developed in [HSY26], together with the generic regularity theory for area-minimizing hypersurfaces established in [CMS23, CMSW25]. Similar ideas are also employed to investigate the Geroch conjecture up to dimension $12$. |
| title | A proof for the Riemannian positive mass theorem up to dimension 19 |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2603.02769 |