2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137612We construct homotopically non-trivial maps from S^m to S^n with arbitrarily small 3-dilation for certain pairs (m,n). The simplest example is m=4, n=3. Other examples include arbitrarily large values of m and n. We show that a homotopy class in pi_7(S^4) can be represented by maps with arbitrarily small 4-dilation if and only if the class is torsion.7 pagesDifferential Geometry53C23text