We show that the traveling salesman problem with a symmetric relaxed Monge matrix as distance matrix is pyramidally solvable and can thus be solved by dynamic programming. Furthermore, we present a polynomial time algorithm that decides whether there exists a renumbering of the cities such that the resulting distance matrix becomes a relaxed Monge matrix.

This article is concerned with geodesics in spaces of Hermitian metrics of positive curvature on an ample line bundle L → X over a Kähler manifold. Stimulated by a recent article of Phong-Sturm [PS], we study the convergence as N → ∞ of geodesics on the finite dimensional symmetric spaces HN of Bergman metrics of ‘height N ’ to Monge-Ampére geodesics on the full infinite dimensional symmetric s...

A Bäcklund transformation between two hyperbolic Monge-Am-p` ere systems may be described as a certain type of exterior differential system on a 6-dimensional manifold B. The transformation is homogeneous if the group of symmetries of the system acts transitively on B. We give a complete classification of homogeneous Bäcklund transformations between hyperbolic Monge-Ampère systems.

This article is concerned with geodesics in spaces of Hermitian metrics of positive curvature on an ample line bundle L → X over a Kähler manifold. Stimulated by a recent article of Phong-Sturm [PS], we study the convergence as N → ∞ of geodesics on the finite dimensional symmetric spaces HN of Bergman metrics of ‘height N ’ to Monge-Ampére geodesics on the full infinite dimensional symmetric s...

We remind of the history of the transportation (Kantorovich) metric and the Monge–Kantorovich problem. We also describe several little-known applications: the first one concerns the theory of decreasing sequences of partitions (tower of measures and iterated metric), the second one relates to Ornstein's theory of Bernoulli automorphisms (¯ d-metric), and the third one is the formulation of the ...

In this paper we study a discrete multi-dimensional version of Aubry-Mather theory. We set this problem as an infinite dimensional linear programming problem and study its relations to Monge-Kantorowich optimal transport. The dual problem turns out to be a discrete analog of the Hamilton-Jacobi equations. As in optimal transport, Monge-Ampére equations also play a role in this problem. We prese...

This note studies the Monge–Ampère Keller–Segel equation in a periodic domain Td(d ≥ 2), a fully nonlinear modification of the Keller–Segel equation where the Monge–Ampère equation det(I + ∇2v) = u + 1 substitutes for the usual Poisson equation ∆v = u. The existence of global weak solutions is obtained for this modified equation. Moreover, we prove the regularity in L∞  0, T ;L∞ ∩W 1,1+γ(Td) ...

This paper studies the pressureless Euler-Poisson system and its fully non-linear counterpart , the Euler-Monge-Ampère system, where the fully non-linear Monge-Ampère equation substitutes for the linear Poisson equation. While the first is a model of plasma physics, the second is derived as a geometric approximation to the Euler incompressible equations. Using energy estimates, convergence of b...

This paper studies the pressureless Euler-Poisson system and its fully non-linear counterpart, the Euler-Monge-Ampère system, where the fully non-linear Monge-Ampère equation substitutes for the linear Poisson equation. While the first is a model of plasma physics, the second is derived as a geometric approximation to the Euler incompressible equations. Using energy estimates, convergence of bo...

with the infinite boundary value condition u = +∞ on ∂Ω. (1.2) We will look for strictly convex solutions in C∞(Ω); it is necessary to assume the underlying domain Ω to be convex for such solutions to exist. This problem was first considered by Cheng and Yau ([5], [6]) for ψ(x, u) = eKuf(x) in bounded convex domains and for ψ(u) = e2u in unbounded domains. More recently, Matero [11] treated the...