2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155568We estimate the second order linking invariants of Lipschitz maps from an n-dimensional ellipse. The estimate uses a new directionally-dependent version of the isoperimetric inequality for cycles inside the ellipse. Using this work, we prove new lower bounds for the k-dilation of maps from one ellipse to another.21 pages, 5 figuresDifferential Geometry53C23text