Vol. 305, No. 1, 2020

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

Keomkyo Seo and Gabjin Yun

Vol. 305 (2020), No. 1, 291–310
Abstract

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 $q=2p-2$ or $q=p$.

Keywords
harmonic form, harmonic map, Liouville-type theorem, weighted manifold
Mathematical Subject Classification 2010
Primary: 53C20
Secondary: 58A10, 58E20