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A note on non-univalent harmonic maps between surfaces

Author(s): Tom Y. H. Wan
Journal: Proc. Amer. Math. Soc. 129 (2001), 567-572.
MSC (2000): Primary 58E20
Posted: October 10, 2000
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Abstract:

We show that a decomposition theorem of Duren-Hengartner about planar harmonic maps can be generalized to give a necessary and sufficient condition for a harmonic map between smooth surfaces to be decomposable as a holomorphic map followed by a univalent harmonic embedding.

References:

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3.: J. Sacks & K. Uhlenbeck, The existence of minimal immersions of 2-sphere, Ann. of Math. 113 (1981) 1-24. MR 82f:58035
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5.: R. Schoen & S. T. Yau, Lectures on harmonic maps, International Press, 1997. MR 98i:58072


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