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Singular Minimal Surfaces

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Geometric Analysis and Nonlinear Partial Differential Equations

Abstract

In this survey I would like to report on some recent results concerning the singular minimal surface equation

$$ div\left( {\frac{{Du}}{{\sqrt {{1 + {{\left| {Du} \right|}^{2}}}} }}} \right)\, = \frac{\alpha }{{u\sqrt {{1 + {{\left| {Du} \right|}^{2}}}} }} $$
(*)

for functions u : Ω → ℝ, Ω ⊂ ℝn a domain, or Ω = ℝn. Here α denotes some real number.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Duisburg, D-47048, Duisburg, Germany

    Ulrich Dierkes

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  1. Ulrich Dierkes
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Editors and Affiliations

  1. Department of Mathematics, University of Bonn, Beringstraße 1, 53115, Bonn, Germany

    Stefan Hildebrandt  & Hermann Karcher  & 

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Dierkes, U. (2003). Singular Minimal Surfaces. In: Hildebrandt, S., Karcher, H. (eds) Geometric Analysis and Nonlinear Partial Differential Equations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55627-2_11

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  • DOI: https://doi.org/10.1007/978-3-642-55627-2_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44051-2

  • Online ISBN: 978-3-642-55627-2

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