an:03944884
Zbl 0588.58017
White, Brian
Infima of energy functionals in homotopy classes of mappings
EN
J. Differ. Geom. 23, 127-142 (1986).
00151067
1986
j
58E20 55Q05
infimum of functionals; [p]-dimensional skeleton; homotopy groups
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.