Summary: Inf-Convolution and Regularization of
Convex Functions on Riemannian Manifolds
of Nonpositive Curvature
Daniel AZAGRA and Juan FERRERA
Departamento de An´alisis Matem´atico
Facultad de Matem´aticas
28040 Madrid -- Spain
Received: December 12, 2005
Accepted: March 27, 2006
We show how an operation of inf-convolution can be used to approximate con-
vex 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.
Key words: inf-convolution, convex function, regularization, Riemannian manifold.
2000 Mathematics Subject Classification: 52A99, 53C99, 49J52, 46T05.