Abstract

In this talk, we provide a sufficient condition under which the method of alternating projections on complete CAT(0) spaces converges strongly. We apply this condition to answer the main question that motivated Bruck’s paper in [10], generalize Prager’s Theorem for Hadamard manifolds, and generalize Sakai’s Theorem for a larger class of the sequences with full measure with respect to Bernoulli measure. Also, we study the method of alternating projections for a nested decreasing sequence of convex sets on Hadamard manifolds and we obtain an alternative proof of the converge of the proximal point method.