Proximal Calculus on Riemannian Manifolds, with Applications to Fixed Point Theory
نویسندگان
چکیده
We introduce a proximal subdifferential and develop a calculus for nonsmooth functions defined on any Riemannian manifold M . We give several applications of this theory, concerning: (1) differentiability and geometrical properties of the distance function to a closed subset C of M ; (2) solvability and implicit function theorems for nonsmooth functions on M ; (3) conditions on the existence of a circumcenter for three different points of M ; and especially (4) fixed point theorems for expansive and nonexpansive mappings and certain perturbations of such mappings defined on M .
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تاریخ انتشار 2004