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Biharmonic maps between surfaces are studied in this paper. We compute the bitension field of a map between surfaces with conformal metrics in complex coordinates. As applications, we show that a linear map from Euclidean plane into $${(\mathbb{R}^2, \sigma^2dwd \bar w)}$$ is always biharmonic if the conformal factor σ is bianalytic; we construct a family of such σ, and we give a classification...
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