On conformal surfaces of annulus type

Details On conformal surfaces of annulus type On conformal surfaces of annulus type

2011-10-24

arxiv.org/abs/1110.5357v4

Mathematics

Differential Geometry

Some typos have been polished and I find that the best constant for L^infinity norm in Wente inequality has been established b

Scientific paper

Let $a>b>0$ and $f$ be a conformal map from $B_a\setminus B_b\subseteq R^2$ into $\R^n$, with $|\nabla f|^2=2e^{2u}$. Then $(e_1, e_2)$ with $e_1=e^{-u}\frac{\partial f}{\partial r},$ and $e_2=r^{-1}e^{-u}\frac{\partial f}{\partial\theta}$ is a moving frame on $f(B_a\setminus B_b)$. It satisfies the following equation $$d\star=0,$$ where $\star$ is the Hodge star operator on $R^2$ with respect to the standard metric. We will study the Dirichret energy of this frame and give some applications.

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