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On the approximation of unstable parametric minimal surfaces

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Abstract

We prove optimal convergence results for discrete approximations to (possibly unstable) minimal surfaces. This appears to be the first class of results of this type for geometric objects solving a highly non-linear geometric variational problem. We introduce a number of new techniques which we expect will be of use in other geometric problems. The theoretical approximation results are confirmed by numerical test computations.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Freiburg, Hermann-Herder-Str. 10, D-79104, Freiburg i.Br., Germany

    Gerhard Dziuk

  2. Department of Mathematics, School of Mathematical Sciences, Australian National University, GPO Box 4, 0200, Canberra, ACT, Australia

    John E. Hutchinson

Authors
  1. Gerhard Dziuk
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  2. John E. Hutchinson
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Dziuk, G., Hutchinson, J.E. On the approximation of unstable parametric minimal surfaces. Calc. Var 4, 27–58 (1996). https://doi.org/10.1007/BF01322308

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