| |
MSRI Summer Microprogram on Nonlinear Partial Differential Equations |
| July 23, 2007 to August 10, 2007 |
| Organized By: L. C. Evans (UC Berkeley, Chair), C. Gutierrez (Temple), C. Sogge (Johns Hopkins), D. Tataru (UC Berkeley) |
| |
| Return to Workshop Description |
| |
Curvature and the continuity of optimal transportation maps
Tuesday July 24, 2007
01:00PM - 01:50PM
Speakers:
Young-Heon Kim
Abstract:
We will discuss the continuity of optimal transport maps, in view of a semi-Riemannian structure which we have formulated recently. A necessary condition for the continuity is given as some non-negativity condition on the curvature of this semi-Riemannian metric, and this result gives a quite general geometric frame work for the regularity theory of Ma, Trudinger, Wang, and Loeper on the potential functions of optimal transport. This is joint work with Robert McCann (University of Toronto).
|
