 
Summary: Mediterr. j. math. 2 (2005), 437450
16605446/04043714, DOI 10.1007/s0000900500564
c 2005 Birkh¨auser Verlag Basel/Switzerland
Mediterranean Journal
of Mathematics
Proximal Calculus on Riemannian Manifolds
Daniel Azagra and Juan Ferrera
Abstract. We introduce a proximal subdifferential and develop a calculus for
nonsmooth functions defined on any Riemannian manifold M. We give some
applications of this theory, concerning, for instance, a BorweinPreiss type
variational principle on a Riemannian manifold M, as well as differentiability
and geometrical properties of the distance function to a closed subset C of
M.
Mathematics Subject Classification (2000). 49J52, 58E30, 58C30, 47H10.
Keywords. Proximal subdifferential, Riemannian manifold, variational princi
ple, mean value theorem.
1. Introduction
The proximal subdifferential of lower semicontinuous realvalued functions is a
very powerful tool which has been extensively studied and used in problems of op
timization, control theory, differential inclusions, Lyapunov Theory, stabilization,
