LJKDeterministic Models and Algorithms: EDPMOISEMGMI Seminar

On Thursday December 1 2016 at 11h00 in Room 106  IMAG Building

Seminary of Mr Roland HILDEBRAND (LJK)

The reach property for selfconcordant barriers

Summary

Let K be a regular convex cone in R^n. A smooth locally strongly convex logarithmically homogeneous function on the interior of the cone is called a selfconcordant barrier if it tends to +infty on the boundary of the cone and satisfies a certain inequality between the second and third derivatives. Selfconcordant barriers can be equivalently described by hyperbolic centroaffine immersions which are asymptotic to the boundary of the cone and have a bounded cubic form. Hyperbolic centroaffine hypersurface immersions in R^n can in turn be seen as positive definite Lagrangian submanifolds of a certain paraKähler space form. The cubic form of the immersion becomes the second fundamental form of the submanifold. We show that Lagrangian submanifolds which arise in this way have the global reach property, with parameter given by a function of the bound of the cubic form.
