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Singularities of harmonic maps. (English) Zbl 0871.58026

This paper surveys research on the existence, structure, behavior, and asymptotics of singularities of harmonic maps. The contents are as follows: 1. The Bochner identity; 2. weak and stationary harmonic maps; 3. partial regularity; 4. extension lemmas; 5. some minimizing tangent maps; 6. continuous maps and relaxed energy; 7. uniqueness of the tangent map; 8. some related areas.
Many important results and recent developments on the existence, regularity and uniqueness of harmonic maps are explained. Moreover, the bibliography is excellent. In summary, a wonderful comprehensive report on singularities of harmonic maps.

MSC:

58E20 Harmonic maps, etc.
35J45 Systems of elliptic equations, general (MSC2000)
35J50 Variational methods for elliptic systems
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References:

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