A priori estimates for the obstacle problem of Hessian type equations on Riemannian manifolds

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We are concerned with a priori estimates for the obstacle problem of a wide class of fully nonlinear equations on Riemannian manifolds. We use new techniques introduced by Bo Guan and derive new results for a priori second order estimates of its singular perturbation problem under fairly general conditions. By approximation, the existence of a C¹,¹ viscosity solution is proved.