Liouville-type theorems for minimal graphs over manifolds
Qi Ding
Abstract
Let $\Sigma$ be a complete Riemannian manifold with the volume doubling property and the uniform Neumann-Poincar$\mathrm{\acute{e}}$ inequality. We show that any positive minimal graphic function on $\Sigma$ is a constant.
Topics & Concepts
MathematicsConstant (computer programming)Riemannian manifoldPoincaré inequalityType (biology)Pure mathematicsMinimal surfaceManifold (fluid mechanics)Property (philosophy)Von Neumann architectureFunction (biology)CombinatoricsInequalityMathematical analysisEvolutionary biologyComputer scienceEpistemologyMechanical engineeringEcologyPhilosophyProgramming languageEngineeringBiologyGeometric Analysis and Curvature FlowsPoint processes and geometric inequalitiesNonlinear Partial Differential Equations