Harmonic maps with defects |
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| Authors: | Brezis Haïm Coron Jean-Michel Lieb Elliott H. |
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| Affiliation: | (1) Département de Mathématiques, Université P. et M. Curie, 4 pl. Jussieu, F-75252 Paris Cedex 05, France;(2) Département de Mathématiques, Ecole Polytechnique, F-91128 Palaiseau Cedex, France;(3) Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France;(4) Present address: Departments of Mathematics and Physics, Princeton University, Jadwin Hall, P.O. Box 708, 08544 Princeton, NJ, USA |
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| Abstract: | Two problems concerning maps  with point singularities from a domain  C  3 toS2 are solved. The first is to determine the minimum energy of when the location and topological degree of the singularities are prescribed. In the second problem is the unit ball and =g is given on  ; we show that the only cases in whichg(x/|x|) minimizes the energy isg=const org(x)=±Rx withR a rotation. Extensions of these problems are also solved, e.g. points are replaced by  holes, 3,S2 is replaced by N,SN–1 or by N, PN–1, the latter being appropriate for the theory of liquid crystals.Work partially supported by U.S. National Science Foundation grant PHY 85-15288-A02 |
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