We study conformal deformation problems on manifolds with boundary which include prescribing sigma-k curvature in the interior. We introduce some conformally covariant multilinear operators as a key technical tool and prove the Dirichlet principle. This result on the sigma-k curvature is parallel to the one that we have observed in an earlier work on the sigma-k Hessian operator. However, the proofs are completely different. This is joint work with Jeffrey Case.