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

Differential Geometry 2026-01-23 v1 Analysis of PDEs

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.

Keywords

Cite

@article{arxiv.2601.15788,
  title  = {A half-space Liouville theorem for anisotropic minimal graph with free boundary},
  author = {Guofang Wang and Wei Wei and Chao Xia and Xuwen Zhang},
  journal= {arXiv preprint arXiv:2601.15788},
  year   = {2026}
}