Generalizations of Weierstrass-type representation formulae and applications

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1.W rewrote the Weierstrass-type representation formula for flat surfaces in hyperbolic 3-space in the form without integration (Darboux-type formula), and classified complete flat surfaces with small numbers of ends. 2.We pointed out the class of ambient spaces for which an analogue of Weierstrass-type (Bryant) representation formula for mean curvature one surfaces in hyperbolic 3-space holds. 3.We found criteria for singularities (cuspidal edges, swallowtails, cuspidal cross caps) which are generic singularities of fronts or frontals. 4.We established fundamental notions of flat fronts in hyperbolic 3-space, and investiagted properties of singularities of such surfaces. 5.We defined a certain class of maximal surfaces with singularities in Minkowski 3-space (called maxface), and investigated their singularities.