Minimal Surfaces

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


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.


Holomorphic Function Minimal Surface Fundamental Form Boundary Curve Profile Curve 
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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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