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p-harmonic 1-forms on complete manifolds |
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| Authors: | Liang-Chu Chang Cheng-Lin Guo Chiung-Jue Anna Sung |
| Affiliation: | 1. Department of Mathematics, National Chung Cheng University, Chiayi, Taiwan, ROC 2. Department of Mathematics, National Cheng Kung University, Tainan, Taiwan 3. Department of Mathematics, National Tsing-Hua University, Hsinchu, Taiwan |
| Abstract: | Let (M m , g) be a complete non-compact manifold with asymptotically non-negative Ricci curvature and finite first Betti number. We prove that any bounded set of p-harmonic 1-forms in L q (M), 0 < q < ∞, is relatively compact with respect to the uniform convergence topology. |
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