2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66712In the present paper we study the Lie sphere geometry of Legendre surfaces by the method of moving frame and we prove an existence theorem for real-analytic Lie-minimal Legendre surfaces.Differential Geometry53A10; 58A15The Cauchy problem for Lie-minimal surfacestext