On conformally invariant equations on Rn

In this paper we provide a complete characterization of fully nonlinear conformally invariant differential operators of any integer order on Rn, which extends the result proved for operators of the second order by A. Li and the first author in Li and Li (2003)  [1]. In particular we prove existence and uniqueness of a family of tensors (suitably invariant under Möbius transformations) which are the basic building blocks that appear in the definition of all conformally invariant differential operators on Rn. We also explicitly compute the tensors that are related to operators of order up to four.