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 H 3 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 H 3 which gives the existence of complete embedded flat surfaces with a finite arbitrary number of isolated singularities.