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arXiv · 2606.01715

A Bernstein-type theorem for capillary graphs in a half-space

Nick Edelen·Chao Li·Jonathan J. Zhu
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Abstract

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.

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Nick Edelen, Chao Li, Jonathan J. Zhu. 2026-06-01. A Bernstein-type theorem for capillary graphs in a half-space. https://arxiv.org/abs/2606.01715

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