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}
}