The Refined Analysis on the Convergence Behavior of Harmonic Map Sequence from Cylinders |
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| Authors: | Li Chen Yuxiang Li Youde Wang |
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| Institution: | 1. Academy of Mathematics and Systematic Sciences, Chinese Academy of Sciences, Beijing, 100190, P.R. China
2. The Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, P.R. China
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| Abstract: | In this paper, we are concerned with the convergence behavior of a sequence of harmonic maps from long cylinders with uniformly bounded energy. If the bubbling phenomenon does not occur, we give the length formula of the limit map (i.e., geodesic in the target manifold). Furthermore, we provide a geometric explanation of the energy identity for a sequence of harmonic maps from degenerating Riemann surfaces with uniformly bounded energy, proved by M. Zhu. |
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