2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/117922We compute the horizontal Hessian of the signed Carnot-Charatheodory distance from a surface S in the Heisenberg group H. The expression for the Hessian is in terms of the surface's intrinsic curvatures. As an application, we compute the horizontal Hessian of the Carnot-Charatheodory distance from a point in H.Analysis of PDEsMetric Geometry49Q15; 53C17; 53C22text