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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.

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  1. Hausdorff Center for Mathematics & Institute for Numerical Simulation, University of Bonn, 53115, Bonn, Germany

    S. Hosseini

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  1. S. Hosseini
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Hosseini, S. Characterization of Lower Semicontinuous Convex Functions on Riemannian Manifolds. Set-Valued Var. Anal 25, 297–311 (2017). https://doi.org/10.1007/s11228-016-0380-9

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