Inf-convolution and regularization of convex functions on Riemannian manifolds of nonpositive curvature

Daniel Azagra; Juan Ferrera

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Inf-convolution and regularization of convex functions on Riemannian manifolds of nonpositive curvature

Daniel Azagra·Juan Ferrera

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Abstract

We show how an operation of inf-convolution can be used to approximate convex functions with $C^{1}$ smooth convex functions on Riemannian manifolds with nonpositive curvature (in a manner that not only is explicit but also preserves some other properties of the original functions, such as ordering, symmetries, infima and sets of minimizers), and we give some applications.

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Daniel Azagra, Juan Ferrera. 2005-05-24. Inf-convolution and regularization of convex functions on Riemannian manifolds of nonpositive curvature. https://arxiv.org/abs/math/0505496

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