On Lp resolvent estimates for elliptic operators on compact manifolds

Abstract. We prove uniform Lp estimates for resolvents of higher order ellip-tic self-adjoint differential operators on compact manifolds without boundary, generalizing a corresponding result of [3] in the case of Laplace – Beltrami oper-ators on Riemannian manifolds. In doing so, we follow the methods, developed in [1] very closely. We also show that spectral regions in our Lp resolvent es-timates are optimal