On Lᵖ resolvent estimates for elliptic operators on compact manifolds

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We prove uniform Lᵖ estimates for resolvents of higher order elliptic self-adjoint differential operators on compact manifolds without boundary, generalizing a corresponding resul of [3] in the case of Laplace-- Beltrami operators 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 estimates are optimal.