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Infima of energy functionals in homotopy classes of mappings. (English) Zbl 0588.58017
The author shows that the infimum of functionals such as $$\int | Df|^ p$$ among $$f: M\to N$$ homotopic to a given map g depends only on the homotopy class of the restriction of g to the [p]-dimensional skeleton of M. For example, if $$M=N$$ and g is the identity map, then the infimum is zero if and only if the first [p] homotopy groups of M are trivial.

##### MSC:
 58E20 Harmonic maps, etc. 55Q05 Homotopy groups, general; sets of homotopy classes
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