On the generalized Weyl problem for flat metrics in the hyperbolic 3-space

The paper deals with the study of complete embedded flat surfaces in H3 with a finite number of isolated singularities. We give a detailed information about its topology, conformal type and metric properties. We show how to solve the generalized Weylʼs problem of realizing isometrically any complete flat metric with Euclidean singularities in H3 which gives the existence of complete embedded flat surfaces with a finite arbitrary number of isolated singularities.