#### 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