Technion - Israel Institute of Technology

Department of Mathematics

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SPECIAL PDE AND APPLIED MATHEMATICS SEMINAR
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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>

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Technion Math. Net (TECHMATH)
Editor: Michael Cwikel   <techm@math.technion.ac.il>
Announcement from: Yehuda Pinchover   <pincho@tx.technion.ac.il>