Technion - Israel Institute of Technology Department of Mathematics =========================================== SPECIAL PDE AND APPLIED MATHEMATICS SEMINAR ============================================Please note the special date, time, and place!!!DATE: Wednesday, March 28, 2012 SPEAKER: Alexander Kolesnikov (Moscow) TITLE: Hessian metrics, $C(N,K)$-spaces, and optimal transportation PLACE: Room 719, Amado Mathematics Building, Technion TIME: 13:30 ABSTRACT: Hessian manifolds are Riemannian manifolds with metrics which can be locally written as the Hessian of a potential function $\Phi$: $g=\mathrm{Hess}\, \Phi$. We consider a special case when $\nabla \Phi$ is the optimal transportation mapping pushing forward a (log-concave) probability measure $\mu$ onto another (log-concave) probability measure. We discuss analytic and geometric properties of the metric-measure space $M=(\mathbb{R}^d, g, \mu)$, and prove, in particular, sufficient conditions for $M$ to belong to the family of $C(N,K)$-spaces. Applications of these results include some dimension-free bounds on the operator norm $\| D^2 \Phi\|$. For further info: Yehuda Pinchover <pincho@techunix.technion.ac.il> For past and future Applied Math/PDE seminars see: <http://www.math.technion.ac.il/pde/seminar.html> --------------------------------------------------------- Technion Math. Net (TECHMATH) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Yehuda Pinchover <pincho@tx.technion.ac.il>