NONDIVERGENT ELLIPTIC-EQUATIONS ON MANIFOLDS WITH NONNEGATIVE CURVATURE

We consider a class of second-order linear elliptic operators, intrins ically defined on Riemannian manifolds, that correspond to nondivergen t operators in Euclidean space. Under the assumption that the sectiona l curvature is nonnegative, we prove a global Krylov-Safonov Harnack i nequality and, as a consequence, a Liouville theorem for solutions of such equations. From the Harnack inequality, we obtain Alexandroff-Bak elman-Pucci estimates and maximum principles for subsolutions. (C) 199 7 John Wiley & Sons, Inc.