3维双曲空间中给定平均曲率曲面的Weierstrass表示

WEIERSTRASS REPRESENTATION FOR SURFACES OF PRESCRIBED MEAN CURVATURE IN THE HYPERBOLIC 3-DIMENSIONAL SPACE

首先叙述双曲空间中曲面的Ｇａｕｓｓ映照的定义；导出Ｇａｕｓｓ映照所满足的Ｂｅｌｔｒａｍｉ方程；给出了给定平均曲率曲面的Ｗｅｉｅｒｓｔｒａｓｓ表示公式；并讨论了这种表示的完全可积条件．

At the first, the author defines the Gauss map for surfaces in the hyperbolic space and prove that the Gauss map must satisfy a Beltrami equation. Next a representation formula for surfaces of prescribed mean curvature is obtained. The author also obtains a partial differential equations of two order for Gauss map and prove that this equation is the complete integrability condition of the above obtained representation.