Viscosity solutions to second order partial differential equations on Riemannian manifolds

We prove comparison, uniqueness and existence results for viscosity solutions nto a wide class of fully nonlinear second order partial differential equations n F(x, u, du, d^{2}u)=0 defined on a finite-dimensional Riemannian manifold n M . Finest results (with hypothesis that require the function F to be ndegenerate elliptic, that is nonincreasing in the second ord..