Liouville-type theorems for minimal graphs over manifolds

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 07 Sep 2021Embargo end date: 01 Jan 2019 English Publisher:Mathematical Sciences PublishersJournal:Analysis & PDE, volume 14, pages 1,925-1,949 (issn: 2157-5045, eissn: 1948-206X,

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Authors: Ding, Qi;

doi: 10.2140/apde.2021.14.1925 , 10.48550/arxiv.1911.10306

arXiv: 1911.10306

Liouville-type theorems for minimal graphs over manifolds

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Abstract

Let $��$ 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 $��$ is a constant.

Related Organizations

Fudan University
China (People's Republic of)

Keywords

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), Mathematics - Differential Geometry, Neumann-Poincaré inequality, Metric Geometry (math.MG), Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Mathematics - Metric Geometry, Differential Geometry (math.DG), Harnack's inequality, Liouville-type theorem, FOS: Mathematics, nonnegative Ricci curvature, minimal graph

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