Trudinger, NeilWang, Xu-Jia2015-12-130944-2669http://hdl.handle.net/1885/93242The Monge mass transfer problem, as proposed by Monge in 1781, is to move points from one mass distribution to another so that a cost functional is minimized among all measure preserving maps. The existence of an optimal mapping was proved by Sudakov in 120012015-12-12