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Minimal Surfaces

  • Andrew Pressley
Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Abstract

In Section 8.4 we considered the problem of finding the shortest paths between two points on a surface. We now consider the analogous problem in one higher dimension, that of finding a surface of minimal area with a fixed curve as its boundary. This is called Plateau’s Problem. The solutions to Plateau’s problem turn out to be surfaces whose mean curvature vanishes everywhere. The study of these so-called minimal surfaces was initiated by Euler and Lagrange in the mid-18th century, but new examples of minimal surfaces have been discovered quite recently.

Keywords

Holomorphic Function Minimal Surface Fundamental Form Boundary Curve Profile Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London 2001

Authors and Affiliations

  • Andrew Pressley
    • 1
  1. 1.Department of MathematicsKing’s CollegeLondonUK

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