A Bernstein-type theorem for capillary graphs in a half-space
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911739386265600 |
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| author | Edelen, Nick Li, Chao Zhu, Jonathan J. |
| author_facet | Edelen, Nick Li, Chao Zhu, Jonathan J. |
| contents | We show that any entire, capillary minimal graph in a half-space must be linear in low-dimensions or, more generally, when some tangent cone at infinity does not split off a vertical line. We also show that the regular set of any entire, capillary-minimizing hypersurface must be connected, and we discuss connections with the one-phase Bernoulli problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01715 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Bernstein-type theorem for capillary graphs in a half-space Edelen, Nick Li, Chao Zhu, Jonathan J. Differential Geometry Analysis of PDEs We show that any entire, capillary minimal graph in a half-space must be linear in low-dimensions or, more generally, when some tangent cone at infinity does not split off a vertical line. We also show that the regular set of any entire, capillary-minimizing hypersurface must be connected, and we discuss connections with the one-phase Bernoulli problem. |
| title | A Bernstein-type theorem for capillary graphs in a half-space |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2606.01715 |