, Volume 24, Issue 2, pp 988-1006

Exotic Minimal Surfaces

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Abstract

We prove a general fusion theorem for complete orientable minimal surfaces in ℝ3 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.

Communicated by Michael Wolf.
Research partially supported by MCYT-FEDER research projects MTM2007-61775 and MTM2011-22547, and Junta de Andalucía Grant P09-FQM-5088.