Theorem shows anisotropic minimal graphs with free boundary in half-space must be flat under growth conditions, indicating importance in geometric analysis.
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 (Arch Rational Mech Anal 32:255–267, 1969) and Simon (Indiana Univ Math J 25:821–855, 1976) to an appropriate free boundary setting.
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Wang et al. (2026) studied this question.
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