### Impacto

Ferrera Cuesta, Juan and Azagra Rueda, Daniel
(2005)
*Proximal calculus on Riemannian manifolds.*
Mediterranean journal of mathematics, 2
(4).
pp. 437-450.
ISSN 1660-5446

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Official URL: http://www.springerlink.com/content/p1q0626q11453542/fulltext.pdf?MUD=MP

## 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.

Item Type: | Article |
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Uncontrolled Keywords: | Proximal subdifferential; Riemannian manifold; Variational principle; Mean value theorem |

Subjects: | Sciences > Mathematics > Mathematical analysis |

ID Code: | 15202 |

References: | H. Attouch and R.J-B. Wets, A convergence theory for saddle functions. Trans. Amer. Math. Soc. 280 (1983), 1-41. D. Azagra and M. Cepedello, Uniform approximation of continuous mappings by smooth mappings with no critical points on Hilbert manifolds. Duke Math. J. 124 (2004), 47-66. D. Azagra and J. Ferrera, Applications of proximal calculus to fixed point theory on Riemannian manifolds. To appear on Nonlinear Anal. D. Azagra, J. Ferrera and F. L´opez-Mesas, Approximate Rolle’s theorems for the proximal subgradient and the generalized gradient. J. Math. Anal. Appl. 283 (2003), 180-191. D. Azagra, J. Ferrera and F. L´opez-Mesas, Nonsmooth analysis and Hamilton-Jacobi equations on Riemannian manifolds. J. Funct. Anal. 220 (2005), 304-361. F.H. Clarke, Yu.S. Ledyaev, R.J. Stern and P.R. Wolenski, Nonsmooth Analysis and Control Theory. Grad. Texts in Math. 178, Springer, 1998. I.Ekeland, Nonconvex minimization problems. Bull. Amer. Math. Soc. (New series) 1 (1979), 443-474. I.Ekeland, The Hopf-Rinow theorem in infinite dimension. J. Differential Geom. 13 (1978), 287-301. W. Klingenberg, Riemannian Geometry, de Gruyter Stud. Math., de Gruyter & Co., Berlin-New York, 1982. C. Mantegazza and A.C. Mennucci, Hamilton-Jacobi equations and distance functions on Riemannian manifolds. Appl. Math. Optim. 47 (2003), 1-25. |

Deposited On: | 11 May 2012 07:11 |

Last Modified: | 06 Feb 2014 10:18 |

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