Liouville type theorems for minimal graphs over manifolds

Abstract

Let $\Sigma$ be a complete Riemannian manifold with the volume doubling property and the uniform Neumann-Poincar$\acute{\mathrm{e}}$ inequality. We show that any positive minimal graphic function on $\Sigma$ is a constant.

References in corpus (1)

• The half-space property and entire positive minimal graphs in M x R

Cited by in corpus (6)

• Bernstein and half-space properties for minimal graphs under Ricci lower bounds
• Non-negative Ricci curvature and Minimal graphs with linear growth
• Recent rigidity results for graphs with prescribed mean curvature
• Half-space Liouville-type theorems for minimal graphs with capillary boundary
• Liouville theorem for minimal graphs over manifolds of nonnegative Ricci curvature
• On splitting complete manifolds via infinity harmonic functions