Fixed Points and Zeros for Set Valued Mappings on Riemannian Manifolds: A Subdifferential Approach

Abstract

In this paper we establish several results which allow to find fixed points and zeros of set-valued mappings on Riemannian manifolds. In order to prove these results we make use of subdifferential calculus. We also give some useful applications.

Whitney's Theorem: A nonsmooth version

“…For this reason we have to introduce some continuity definitions for such kind of functions. For a deep study of set-valued functions see [4] or [6].…”

“…For an introduction to the subdifferential of a function defined on a manifold, see [2] for instance. In [3] set-valued functions on manifolds are studied. In the sequel M stand for a C 1 finite dimensional manifold.…”