On conformally invariant equations on {$\bold{R}^n$}

In this paper we provide a complete characterization of fully nonlinear conformally invariant differential operators of any integer order on {$\bold{R}^n$}, 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 {$\bold{R}^n$}. We also explicitly compute the tensors that are related to operators of order up to four.