On the moving frame of a conformal map from 2-disk into {\mathbb{R}^n}

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 \({\int_B |K_{f}| d\mu_f < 2\pi}\) .