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

Daniel Azagra·Juan Ferrera
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Abstract

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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Daniel Azagra, Juan Ferrera. 2004-03-26. Proximal calculus on Riemannian manifolds, with applications to fixed point theory. https://arxiv.org/abs/math/0403465

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