On the continuity of the total cost in the mass transport problem with relativistic cost functions

TL;DR

This paper proves the continuity of total cost in relativistic mass transport problems and provides estimates on mass movement directions, extending recent results and addressing open questions in the field.

Contribution

It establishes the continuity of total cost for relativistic costs and offers general estimates on mass movement directions under mild assumptions, generalizing prior work.

Findings

Proves continuity of total cost in relativistic mass transport.

Provides estimates on directions of mass movement.

Answers open questions from recent related research.

Abstract

In this paper we consider the mass transport problem in the case of a relativistic cost; we can establish the continuity of the total cost, together with a general estimate about the directions in which the mass can actually move, under mild assumptions. These results generalize those recently obtained by J.Bertrand, A.Pratelli and M.Puel, also positively answering some of the open questions there.