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We show how an operation of inf-convolution can be used to approximate con vex functions with C 1 smooth convex functions on Riemannian manifolds with  nonpositive curvature (in a manner that not only is explicit but also preserves  some other properties of the original functions, such as ordering, symmetries,  infima and sets of minimizers), and we give some applications.We show how an operation of inf-convolution can be used to approximate convex functions with C1 smooth convex functions on Riemannian manifolds with nonpositive curvature (in a manner that not only is explicit but also preserves some other properties of the original functions, such as ordering, symmetries, infima and sets of minimizers), and we give some applications

Inf-Convolution and Regularization of Convex Functions on Riemannian Manifolds of Nonpositive Curvature