  We prove the existence of classical solutions to the Dirichlet problem for a
class of fully nonlinear elliptic equations of curvature type on Riemannian
manifolds. We also derive new second derivative boundary estimates which allows
us to extend some of the existence theorems of Caffarelli, Nirenberg and Spruck
[4] and Ivochkina, Trundinger and Lin [19] to more general curvature functions
and less convex domains.
