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 Borwein-Preiss 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.
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The first-named author was supported by a Marie Curie Intra-European Fellowship of the European Community, Human Resources and Mobility Programme under contract number MEIF CT2003-500927. The second-named author was supported by BFM2003-06420.
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Azagra, D., Ferrera, J. Proximal Calculus on Riemannian Manifolds. MedJM 2, 437–450 (2005). https://doi.org/10.1007/s00009-005-0056-4
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DOI: https://doi.org/10.1007/s00009-005-0056-4