2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139890We give an analytical proof of the Poincare-type inequalities for widths of geodesic homotopies between equivariant maps valued in Hadamard metric spaces. As an application we obtain a linear bound for the length of an element conjugating two finite lists in a group acting on an Hadamard space.minor stylistic corrections; 15 pagesGeometric TopologyAnalysis of PDEsMetric Geometry53C23; 58E20; 20F65.On geodesic homotopies of controlled width and conjugacies in isometry groupstext