#### Vol. 14, No. 6, 2021

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Liouville-type theorems for minimal graphs over manifolds

### Qi Ding

Vol. 14 (2021), No. 6, 1925–1949
##### Abstract

Let $\Sigma$ be a complete Riemannian manifold with the volume-doubling property and the uniform Neumann–Poincaré inequality. We show that any positive minimal graphic function on $\Sigma$ is constant.

##### Keywords
minimal graph, nonnegative Ricci curvature, Liouville-type theorem, Harnack's inequality, Neumann–Poincaré inequality
##### Mathematical Subject Classification 2010
Primary: 53A10, 53C21