Exotic Minimal Surfaces

Abstract

We prove a general fusion theorem for complete orientable minimal surfaces in ${\mathbb{R}}^3$ with finite total curvature. As a consequence, complete orientable minimal surfaces of weak finite total curvature with exotic geometry are produced. More specifically, universal surfaces (i.e., surfaces from which all minimal surfaces can be recovered) and space-filling surfaces with arbitrary genus and no symmetries.

16 pages, 3 figures