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Here, the domain is the universal cover of the punctured Riemann surface obtained from a conformal completion of $X$. Moreover, such a harmonic map is unique if one prescribes, in addition, the principal part of the Hopf differential at each puncture. 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Here, the domain is the universal cover of the punctured Riemann surface obtained from a conformal completion of $X$. Moreover, such a harmonic map is unique if one prescribes, in addition, the principal part of the Hopf differential at each puncture. 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