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arXiv · 2601.15788

A half-space Liouville theorem for anisotropic minimal graph with free boundary

Guofang Wang·Wei Wei·Chao Xia·Xuwen Zhang
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Abstract

In this paper we prove the following Liouville-type theorem: any anisotropic minimal graph with free boundary in the half-space must be flat, provided that the graph function has at most one-sided linear growth. This extends the classical results of Bombieri-De Giorgi-Miranda and Simon to an appropriate free boundary setting.

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Guofang Wang, Wei Wei, Chao Xia, Xuwen Zhang. 2026-01-22. A half-space Liouville theorem for anisotropic minimal graph with free boundary. https://arxiv.org/abs/2601.15788

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