Orateur
Description
The classical Monge-Kantorovich (transportation) problem deals with measures on a product of two spaces with two independent fixed marginals. Its natural generalization (multimarginal Monge-Kantorovich problem) deals with the products of n spaces X_1, ..., X_n with n independent marginals. We study the Monge-Kantorovich problem on X_1 \times X_2 ... \times ... X_n with fixed projections onto the products of X_{i_1} , ... X_{i_k} for all k-tuples of indices (k<n). On the language of descriptive geometry this can be called "k-dimensional Monge's protocols for n-dimensional bodies". There are both similarities and differences from the classical problem concerning feasibility, uniqueness, smoothness, duality theorem, existence of the dual solution.
