We show how an operation of inf-convolution can be used to approximate convex functions with C1 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.
@article{urn:eudml:doc:41905,
title = {Inf-convolution and regularization of convex functions on Riemannian manifolds of nonpositive curvature.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {19},
year = {2006},
pages = {323-345},
zbl = {1126.53022},
mrnumber = {MR2241434},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41905}
}
Azagra, Daniel; Ferrera, Juan. Inf-convolution and regularization of convex functions on Riemannian manifolds of nonpositive curvature.. Revista Matemática de la Universidad Complutense de Madrid, Tome 19 (2006) pp. 323-345. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41905/