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 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