On the moving frame of a conformal map from 2-disk into {\mathbb{R}^n} |
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| Authors: | Yuxiang Li Yong Luo Hongyan Tang |
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| Institution: | 1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China
2. Mathematisches Institut, Albert-Ludwigs-Universit?t Freiburg, Eckerstr. 1, 79104, Freiburg, Germany
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| 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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