LIOUVILLE-TYPE THEOREMS FOR WEIGHTED p-HARMONIC 1-FORMS AND WEIGHTED p-HARMONIC MAPS

초록

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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