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LIOUVILLE-TYPE THEOREMS FOR WEIGHTED p-HARMONIC 1-FORMS AND WEIGHTED p-HARMONIC MAPS
- Authors
- Seo, Keomkyo; Yun, Gabjin
- Issue Date
- Mar-2020
- Publisher
- PACIFIC JOURNAL MATHEMATICS
- Keywords
- harmonic form; harmonic map; Liouville-type theorem; weighted manifold
- Citation
- PACIFIC JOURNAL OF MATHEMATICS, v.305, no.1, pp 291 - 310
- Pages
- 20
- Journal Title
- PACIFIC JOURNAL OF MATHEMATICS
- Volume
- 305
- Number
- 1
- Start Page
- 291
- End Page
- 310
- ISSN
- 0030-8730
- Abstract
- In this paper, we obtain Bochner-Weitzenbock 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 non-compact manifold with non-negative Bakry-Emery Ricci curvature, where q =2p - 2 or q = p.
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