In the mathematical field of differential geometry, the Paneitz operator is a fourth-order differential operator defined on a Riemannian manifold of dimension n. It is named after , who discovered it in 1983, and whose preprint was later published posthumously in . In fact, the same operator was found earlier in the context of conformal supergravity by and in 1982(Phys Lett B 110 (1982) 117 and Nucl Phys B 1982 (1982) 157 ).It is given by the formula where Δ is the positive Laplacian. In four dimensions this yields the .