Set-Valued and Variational Analysis

, Volume 25, Issue 2, pp 297–311 | Cite as

Characterization of Lower Semicontinuous Convex Functions on Riemannian Manifolds

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Abstract

In this paper, an upper subderivative of a lower semicontinuous function on a Riemannian manifold is introduced. Then, an approximate mean value theorem for the upper subderivative on a Hadamard manifold is presented. Moreover, the results are used for characterization of convex functions on Riemannian manifolds.

Keywords

Riemannian manifolds Subdifferential Lower semicontinuous functions Locally Lipschitz functions 

Mathematics Subject Classification (2010)

58C05 49J52 47H05 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Hausdorff Center for Mathematics & Institute for Numerical SimulationUniversity of BonnBonnGermany

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