  We study a class of three-point functions on the de Sitter universe and on
the asymptotic cone. A blending of geometrical ideas and analytic methods is
used to compute some remarkable integrals, on the basis of a generalized
star-triangle identity living on the cone and on the complex de Sitter
manifold. We discuss an application of the general results to the study of the
stability of scalar particles on the Sitter universe.
