Abstract
We prove the harmonic map version of the Royden decomposition in the sense that given any bounded C 1-map f with finite total energy on a complete Riemannian manifold into a Cartan-Hadamard manifold, there exists a unique bounded harmonic map with finite total energy from the manifold into the Cartan-Hadamard manifold taking the same boundary value at each harmonic boundary point as that of f.
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This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2012006926).
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Lee, Y.H. Royden Decomposition for Harmonic Maps with Finite Total Energy. Results Math 71, 687–692 (2017). https://doi.org/10.1007/s00025-015-0503-x
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DOI: https://doi.org/10.1007/s00025-015-0503-x