Abstract
Let f be a conformal map from the 2-disk into \({\mathbb{R}^n}\) . We prove that the image f(B) have a normal tangent vector basis (e 1, e 2) with \({\|d(e_{1}, e_{2})\|_{L^2(B)} \leq C\|A\|_{L^2(B)}}\) when the total Gauss curvature \({\int_B |K_{f}| d\mu_f < 2\pi}\) .
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Communicated by F. Helein.
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Li, Y., Luo, Y. & Tang, H. On the moving frame of a conformal map from 2-disk into \({\mathbb{R}^n}\) . Calc. Var. 46, 31–37 (2013). https://doi.org/10.1007/s00526-011-0471-2
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DOI: https://doi.org/10.1007/s00526-011-0471-2