Approximation theory for non-orientable minimal surfaces and applications

Abstract

We prove a version of the classical Runge and Mergelyan uniform approximation theorems for non-orientable minimal surfaces in Euclidean 3-space R3. Then, we obtain some geometric applications. Among them, we emphasize the following ones: 1. A Gunning-Narasimhan type theorem for non-orientable conformal surfaces. 2. An existence theorem for non-orientable minimal surfaces in R3, with arbitrary conformal structure, properly projecting into a plane. 3. An existence result for non-orientable minimal surfaces in R3 with arbitrary conformal structure and Gauss map omitting one projective direction.

34 pages, 4 figures

References in corpus (2)

• Null curves and directed immersions of open Riemann surfaces
• Complete non-orientable minimal surfaces in ${\mathbb{R}}^3$ and asymptotic behavior

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