Infima of energy functionals in homotopy classes of mappings. (English) Zbl 0588.58017

White, Brian

J. Differ. Geom. 23, 127-142 (1986).

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

Keywords:

infimum of functionals; [p]-dimensional skeleton; homotopy groups