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The Barrier Principle for Minimal Submanifolds of Arbitrary Codimension

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Abstract

We establish a barrier principle for minimal submanifolds of a Riemannianmanifold of arbitrary codimension. We construct examples of barriers fortwo-dimensional minimal surfaces in ℝn, n ≥ 4, and apply these to deduceexistence as well as nonexistence theorems for Plateau's problem.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal do Ceará, Campus do Pici, 60455-760, Fortaleza-Ce, Brazil

    Luquésio P. Jorge

  2. Mathematisches Institut, Universität Heidelberg, Im Neuenheimer Feld 288, 69120, Heidelberg, Germany

    Friedrich Tomi

Authors
  1. Luquésio P. Jorge
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  2. Friedrich Tomi
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Jorge, L.P., Tomi, F. The Barrier Principle for Minimal Submanifolds of Arbitrary Codimension. Annals of Global Analysis and Geometry 24, 261–267 (2003). https://doi.org/10.1023/A:1024791501324

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  • DOI: https://doi.org/10.1023/A:1024791501324

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