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The Least Gradient Method for Computing Area-Minimizing Hypersurfaces

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Statistical Thermodynamics and Differential Geometry of Microstructured Materials

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 51))

Abstract

In this paper we give a brief presentation of the least gradient method for computing area-minimizing hypersurfaces. The theoretical basis for the method can be found in the author’s papers [5] and [6], and a detailed discussion of the implementation in [7]. These papers are rather heavy reading because of the technical details included. To some extent technical details are inevitable, but in this paper we shall try to minimize them.

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References

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  8. H.R. Parks & W. P. Ziemer, Jacobi fields and regularity of functions of least gradient, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Serie IV, 11 (1984), pp. 505–527.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Oregon State University, Corvallis, OR, 97331, USA

    Harold R. Parks

Authors
  1. Harold R. Parks
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering and Materials Science, University of Minnesota, 55455, Minneapolis, MN, USA

    H. Ted Davis

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

    Johannes C. C. Nitsche

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© 1993 Springer-Verlag New York, Inc.

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Parks, H.R. (1993). The Least Gradient Method for Computing Area-Minimizing Hypersurfaces. In: Davis, H.T., Nitsche, J.C.C. (eds) Statistical Thermodynamics and Differential Geometry of Microstructured Materials. The IMA Volumes in Mathematics and its Applications, vol 51. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8324-6_7

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  • DOI: https://doi.org/10.1007/978-1-4613-8324-6_7

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8326-0

  • Online ISBN: 978-1-4613-8324-6

  • eBook Packages: Springer Book Archive

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