Liouville-type theorems for minimal graphs over manifolds

Ding, Qi

doi:10.2140/apde.2021.14.1925

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Liouville-type theorems for minimal graphs over manifolds

Qi Ding

Vol. 14 (2021), No. 6, 1925–1949

DOI: 10.2140/apde.2021.14.1925

Abstract

Let $Σ$ 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 $Σ$ is constant.

Keywords

minimal graph, nonnegative Ricci curvature, Liouville-type theorem, Harnack's inequality, Neumann–Poincaré inequality

Mathematical Subject Classification 2010

Primary: 53A10, 53C21

Milestones

Received: 3 October 2019

Accepted: 25 March 2020

Published: 7 September 2021

Authors

Qi Ding
Shanghai Center for Mathematical Sciences Fudan University Shanghai China

Vol. 14, No. 6, 2021