White, Brian Infima of energy functionals in homotopy classes of mappings. (English) Zbl 0588.58017 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. Cited in 1 ReviewCited in 47 Documents MSC: 58E20 Harmonic maps, etc. 55Q05 Homotopy groups, general; sets of homotopy classes Keywords:infimum of functionals; [p]-dimensional skeleton; homotopy groups PDF BibTeX XML Cite \textit{B. White}, J. Differ. Geom. 23, 127--142 (1986; Zbl 0588.58017) Full Text: DOI OpenURL