L p-Theory of elliptic differential operators on manifolds of bounded geometry

This paper is devoted to some of the properties of uniformly elliptic differential operators with bounded coefficients on manifolds of bounded geometry in L pspaces. We prove the coincidence of minimal and maximal extensions of an operator of a considered type with a positive principal symbol, the existence of holomorphic semigroup, generated by it, and the estimates of L p-norms of the operators of this semigroup. Some spectral properties of such operators in L pspaces are also studied.