Surfaces which possess Weierstrass-type representationformula and their singularities

研究了具有weierstrass型表示公式的曲面的性质。对于欧几里得3空间中的极小曲面和双曲3空间中的常平均曲率1曲面，构造了高属实例。对于Minkowski三维空间中的类空间极大曲面和de Sitter三维空间中的类空间常平均曲率1曲面，研究了奇异点和端点的行为。此外，研究了Minkowski三维空间中的零平均曲率曲面，构造了一些非平凡的嵌入。

Properties of surfaces which possess Weierstrass-type representation formula are investigated. For minimal surfaces in Euclidean 3-space and constant mean curvature 1 surfaces in hyperbolic 3-space, higher genus examples are constructed. For spacelike maximal surfaces in Minkowski 3-space and spacelike constant mean curvature 1 surfaces in de Sitter 3-space,the behavior of singularities and ends are investigated. Moreover, zero mean curvature surfaces in Minkowski 3-space are investigated and some non-trivial embedding are constructed.