Calibrations and New Singularities in Area-minimizing Surfaces: A Survey

  • Frank Morgan
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 4)


In the past ten years the theory of calibrations has shed much light on the behavior of m-dimensional area-minimizing submanifolds of n-dimensional spaces. (Area-minimizing means that no other submanifold with the same boundary, or alternatively in the same homology class, has less m-dimensional area.) Area-minimizing submanifolds often have interesting singularities. An early obstacle to understanding was the difficulty of establishing that any singular example actually was area-minimizing. Calibrations produce a rich variety of such examples, as indicated in §3.


Sectional Curvature Angle Criterion Fundamental Theorem Homology Class Geometric Measure Theory 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Frank Morgan
    • 1
  1. 1.Dept. of MathematicsWilliams CollegeWilliamstownUSA

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