Liouville-type theorems for weighted p-harmonic 1-forms and weighted p-harmonic maps

In this paper, we obtain Bochner–Weitzenböck formulas for the weighted Hodge Laplacian operator acting on differential forms and more generally on vector bundle-valued weighted $p$ -harmonic forms. Applying these formulas, we prove Liouville-type theorems for weighted $L^{q}$ $p$ -harmonic $1$ -forms and for weighted $p$ -harmonic maps in a weighted complete noncompact manifold with nonnegative Bakry–Émery Ricci curvature, where $q = 2 p - 2$ or $q = p$ .

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Keywords

harmonic form, harmonic map, Liouville-type theorem, weighted manifold

Mathematical Subject Classification 2010

Primary: 53C20

Secondary: 58A10, 58E20

Milestones

Received: 30 April 2018

Revised: 17 February 2019

Accepted: 31 October 2019

Published: 17 March 2020

Authors

Keomkyo Seo
Department of Mathematics Sookmyung Women’s University Yongsan-gu Seoul South Korea

Gabjin Yun
Department of Mathematics Myong Ji University Cheoin-gu Yong-In South Korea

Vol. 305, No. 1, 2020

Keomkyo Seo and Gabjin Yun

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors