Theorems on Regularity and Singularity of Energy Minimizing Maps

1. Front Matter

   Pages i-vii

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2. Analytic Preliminaries

   • Leon Simon

   Pages 1-18

3. Regularity Theory for Harmonic Maps

   • Leon Simon

   Pages 19-50

4. Approximation Properties of the Singular Set

   • Leon Simon

   Pages 51-90

5. Rectihability of the Singular Set

   • Leon Simon

   Pages 91-146

6. Back Matter

   Pages 147-152

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The aim of these lecture notes is to give an essentially self-contained introduction to the basic regularity theory for energy minimizing maps, including recent developments concerning the structure of the singular set and asymptotics on approach to the singular set. Specialized knowledge in partial differential equations or the geometric calculus of variations is not required; a good general background in mathematical analysis would be adequate preparation.

• Calculus of Variations
• Riemannian manifold
• differential equation
• geometric calculus
• partial differential equation

• Department of Mathematics, Stanford University, Stanford, USA

  Leon Simon

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