  We propose the first global accelerated gradient method for Riemannian
manifolds. Toward establishing our result we revisit Nesterov's estimate
sequence technique and develop an alternative analysis for it that may also be
of independent interest. Then, we extend this analysis to the Riemannian
setting, localizing the key difficulty due to non-Euclidean structure into a
certain ``metric distortion.'' We control this distortion by developing a novel
geometric inequality, which permits us to propose and analyze a Riemannian
counterpart to Nesterov's accelerated gradient method.
