Singularities of a surface given by Kenmotsu-type formula in Euclidean three-space (Q2279003)

The authors study singularities of surfaces which are given by Kenmotsu-type formulae with prescribed unbounded mean curvature. The Kenmotsu-type formula is a coordinate free formula that describes immersed surfaces in the Euclidean 3-space with prescribed mean curvature and Gauss map. In this light, the authors investigate a similar formula for singular surfaces equipped with the same conditions. Finally, they calculate geometric invariants of cuspidal edges and swallowtails.