Boundary Operators Associated with the Sixth-Order GJMS Operator

We describe a set of conformally covariant boundary operators associated with the 6th-order Graham - Jenne - Mason - Sparling (GJMS) operator on a conformally invariant class of manifolds that includes compactifications of Poincaré-Einstein manifolds. This yields a conformally covariant energy functional for the 6th-order GJMS operator on such manifolds. Our boundary operators also provide a new realization of the fractional GJMS operators of order one, three, and five as generalized Dirichlet-to-Neumann operators. This allows us to prove some sharp Sobolev trace inequalities involving the interior $W^{3,2}$-seminorm, including an analogue of the Lebedev-Milin inequality on six-dimensional manifolds.