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This article studies the Dirichlet problem for a class of degenerate fullynonlinear elliptic equations on Riemannian manifolds with \textit{mean concave}boundary in the sense that the mean curvature of the boundary is\textit{nonpositive}. The proof is primarily based on a quantitative boundaryestimate. Also, we obtain analogous results in complex variables. In Appendix,the subsolutions are also constructed on certain topologically productmanifolds.

The Dirichlet problem for a class of degenerate fully nonlinear elliptic equations on Riemannian manifolds with mean concave boundary