Approximation theory for nonorientable minimal surfaces and applications

We prove a version of the classical Runge and Mergelyan uniform approximation theorems for nonorientable minimal surfaces in Euclidean 3-space R-3. Then we obtain some geometric applications. Among them, we emphasize the following ones: A Gunning-Narasimhan-type theorem for nonorientable conformal surfaces. An existence theorem for nonorientable minimal surfaces in R-3 with arbitrary conformal structure, properly projecting into a plane. An existence result for nonorientable minimal surfaces in R-3 with arbitrary conformal structure and Gauss map omitting one projective direction.