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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.

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Notes

  1. Notice that \(U_{P}=U_{P}^{0}\) for all \(P \in z_{0}^{-1}(z_{0}(B_{0} \cup E_{0}))\).

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Authors and Affiliations

  1. Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    Francisco J. López

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  1. Francisco J. López
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Correspondence to Francisco J. López.

Additional information

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.

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López, F.J. Exotic Minimal Surfaces. J Geom Anal 24, 988–1006 (2014). https://doi.org/10.1007/s12220-012-9361-x

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  • DOI: https://doi.org/10.1007/s12220-012-9361-x

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