Surfaces which possess Weierstrass-type representationformula and their singularities

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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.