Asymptotics of high-codimensional area-minimizing currents in hyperbolic space
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908761169330176 |
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| author | Jiang, Xumin Xie, Jiongduo |
| author_facet | Jiang, Xumin Xie, Jiongduo |
| contents | We investigate the asymptotic behavior of high-codimensional area-minimizing locally rectifiable currents in hyperbolic space, addressing a problem posed by F.H. Lin and establishing ``boundary regularity at infinity" results for such currents near their asymptotic boundaries under the standard Euclidean metric. Intrinsic obstructions to high-order regularity arise for odd-dimensional minimal surfaces, revealing a constraint dependent on the geometry of the asymptotic boundary. Our work advances the asymptotic theory of high-codimensional minimal surfaces in hyperbolic space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04027 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotics of high-codimensional area-minimizing currents in hyperbolic space Jiang, Xumin Xie, Jiongduo Differential Geometry We investigate the asymptotic behavior of high-codimensional area-minimizing locally rectifiable currents in hyperbolic space, addressing a problem posed by F.H. Lin and establishing ``boundary regularity at infinity" results for such currents near their asymptotic boundaries under the standard Euclidean metric. Intrinsic obstructions to high-order regularity arise for odd-dimensional minimal surfaces, revealing a constraint dependent on the geometry of the asymptotic boundary. Our work advances the asymptotic theory of high-codimensional minimal surfaces in hyperbolic space. |
| title | Asymptotics of high-codimensional area-minimizing currents in hyperbolic space |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2601.04027 |