Foliation of area-minimizing hypersurfaces in asymptotically flat manifolds of higher dimension
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914378732797952 |
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| author | He, Shihang Shi, Yuguang Yu, Haobin |
| author_facet | He, Shihang Shi, Yuguang Yu, Haobin |
| contents | We prove the existence of foliations by area-minimizing hypersurfaces in asymptotically flat (AF) manifolds with arbitrary dimension and arbitrary ends. Also we provide behaviors of those hypersurfaces near the infinity of AF ends and demonstrate that the singular set of those area-minimizing hypersurfaces is outside AF ends (cf Theorem \ref{thm: foliation}). Building on the positive mass theorem for AF manifolds with arbitrary ends, we establish a global behavior for free-boundary area-minimizing hypersurfaces inside coordinate cylinders in AF manifolds of dimension less than or equal to $8$ (cf. Theorem \ref{thm: 8dim Schoen conj}) |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07681 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Foliation of area-minimizing hypersurfaces in asymptotically flat manifolds of higher dimension He, Shihang Shi, Yuguang Yu, Haobin Differential Geometry 53C21, 53C24 We prove the existence of foliations by area-minimizing hypersurfaces in asymptotically flat (AF) manifolds with arbitrary dimension and arbitrary ends. Also we provide behaviors of those hypersurfaces near the infinity of AF ends and demonstrate that the singular set of those area-minimizing hypersurfaces is outside AF ends (cf Theorem \ref{thm: foliation}). Building on the positive mass theorem for AF manifolds with arbitrary ends, we establish a global behavior for free-boundary area-minimizing hypersurfaces inside coordinate cylinders in AF manifolds of dimension less than or equal to $8$ (cf. Theorem \ref{thm: 8dim Schoen conj}) |
| title | Foliation of area-minimizing hypersurfaces in asymptotically flat manifolds of higher dimension |
| topic | Differential Geometry 53C21, 53C24 |
| url | https://arxiv.org/abs/2603.07681 |