Abstract
In 1936 H. Lewy showed that the Jacobian determinant of a harmonic homeomorphism between planar domains does not vanish and thus the map is a diffeomorphism. This built on the earlier existence results of Radó and Kneser. R. Shoen and S.T. Yau generalised this result to degree 1 harmonic mappings between closed Riemann surfaces. Here we give a new approach that establishes all these results in complete generality.
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