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In this paper, we prove a new gradient estimate for minimal graphs defined on domains of a complete manifold   $M$   with Ricci curvature bounded from below. This enables us to show that positive, entire minimal graphs on manifolds with non-negative Ricci curvature are constant and that complete, parabolic manifolds with Ricci curvature bounded from below have the half-space property. We avoid the need of sectional curvature bounds on   $M$   by exploiting a form of the Ahlfors–Khas’minskii duality in nonlinear potential theory.

Bernstein and Half-Space Properties for Minimal Graphs Under Ricci Lower Bounds