Proximal calculus on Riemannian manifolds, with applications to fixed point theory

Details Proximal calculus on Riemannian manifolds, with applications to fixed point theory Proximal calculus on Riemannian manifolds, with applications to fixed point theory

2004-03-26

arxiv.org/abs/math/0403465v1

Mathematics

Differential Geometry

27 pages

Scientific paper

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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