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Minimal surfaces with isolated singularities

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Abstract

For n≥3, there exists an embedded minimal hypersurface in Rn+1 which has an isolated singularity but which is not a cone. Each example constructed here is asymptotic to a given, completely arbitrary, nonplanar minimal cone and is stable in case the cone satisfies a strict stability inequality.

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Authors and Affiliations

  1. Mathematics Department, University of Chicago, 60637, Chicago, IL, USA

    Luis Caffarelli

  2. School of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA

    Robert Hardt

  3. Centre for Mathematical Analysis, Australian National University, G.P.O. Box 4, 2001, Canberra, A.C.T., Australia

    Leon Simon

Authors
  1. Luis Caffarelli
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  2. Robert Hardt
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  3. Leon Simon
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Research partially supported by the National Science Foundation

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Caffarelli, L., Hardt, R. & Simon, L. Minimal surfaces with isolated singularities. Manuscripta Math 48, 1–18 (1984). https://doi.org/10.1007/BF01168999

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  • DOI: https://doi.org/10.1007/BF01168999

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