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Counting Singularities in Liquid Crystals

  • Frederick J. AlmgrenJr.
  • Elliott H. Lieb
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 4)

Abstract

Energy minimizing harmonic maps from the ball to the sphere arise in the study of liquid crystal geometries and in the classical nonlinear sigma model. We linearly dominate the number of points of discontinuity of such a map by the energy of its boundary value function. Our bound is optimal (modulo the best constant) and is the first bound of its kind. We also show that the locations and numbers of singular points of minimizing maps is often counterintuitive; in particular, boundary symmetries need not be respected.

Keywords

Liquid Crystal Singular Point Boundary Energy Finite Energy Cayley Tree 
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 Science+Business Media New York 1990

Authors and Affiliations

  • Frederick J. AlmgrenJr.
    • 1
  • Elliott H. Lieb
    • 1
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

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