Riesz-Martin representation for positive super-polyharmonic functions in A Riemannian manifold

Letube a super-biharmonic function, that is,Δ2u≥0, on the unit discDin the complex plane, satisfying certain conditions. Then it has been shown thatuhas a representation analogous to the Poisson-Jensen representation for subharmonic functions onD. In the same vein, it is shown here that a functionuon any Green domainΩin a Riemannian manifold satisfying the conditions(−Δ)iu≥0for0≤i≤mhas a representation analogous to the Riesz-Martin representation for positive superharmonic functions onΩ.