Vol. 14, No. 6, 2021

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 6, 1671–1976
Issue 5, 1333–1669
Issue 4, 985–1332
Issue 3, 667–984
Issue 2, 323–666
Issue 1, 1–322

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
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