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Minimal Surfaces

  • Book
  • © 2011
  • Latest edition

Overview

Authors:
  1. Ulrich Dierkes

    1. Campus Duisburg, University of Duisburg Faculty of Mathematics, Duisburg, Germany

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  2. Stefan Hildebrandt

    1. University of Bonn Mathematical Institute, Bonn, Germany

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  3. Friedrich Sauvigny

    1. LS Analysis, Brandenburgian Technical University Mathematical Institute, Cottbus, Germany

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  4. Anthony Tromba

    1. University of California at Santa Cruz Department of Mathematics, Santa Cruz, USA

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Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 339-341)

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Keywords

  • 49Q05,53A05, 53A07, 53B20, 35J20, 35J47, 35J50, 35J75, 49Q20
  • calculus of variations
  • conformal mappings
  • differential geometry
  • minimal surfaces
  • regularity theory
  • partial differential equations

About this book

The three-volume treatise consists of the volumes Minimal Surfaces (GL 339), Regularity of Minimal Surfaces (GL 340), and Glolbal Theory of Minimal Surfaces (GL 341) that replace the monograph Minimal Surfaces I , II, published as volumes 295 and 296  of the Grundlehren der mathematischen Wissenschaft series.

Ther first volume covers the classical theory as well as existence results concerning boundary value problems for minimal surfaces, in particular results for Plateau's problem.

The second volume deals with basic regularity results for minimal surfaces concerning their boundary behaviour at Plateau boundaries and free boundaries. Moreover, exclosure theorems, isoperimetricc inequalities and existence theorems for surfaces of prescribed mean curvature in a Riemanian manifold and for the thread problem are discussed.

Finally, the third volume deals with geometric properties of minimal surfaces with free boundaries and with a priori gradient estimates for n-dimensional minimal surfaces, leading to various Bernstein-type theorems. Secondly, a global theory of minimal surfaces (as envisioned by Smale) is presented, including index theorems.

Authors and Affiliations

  • Campus Duisburg, University of Duisburg Faculty of Mathematics, Duisburg, Germany

    Ulrich Dierkes

  • University of Bonn Mathematical Institute, Bonn, Germany

    Stefan Hildebrandt

  • LS Analysis, Brandenburgian Technical University Mathematical Institute, Cottbus, Germany

    Friedrich Sauvigny

  • University of California at Santa Cruz Department of Mathematics, Santa Cruz, USA

    Anthony Tromba

Bibliographic Information

  • Book Title: Minimal Surfaces

  • Authors: Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny, Anthony Tromba

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • Publisher: Springer Berlin, Heidelberg

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2011

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 2

  • Number of Pages: L, 1910

  • Additional Information: Originally published as volumes 295 and 296 in series: Grundlehren der mathematischen Wissenschaft series

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