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.


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