I would appreciate help understanding Kantorovich's 1942 paper on translocation on masses.
The English translation can be found here: http://web.eecs.umich.edu/~pettie/matching/Kantorovitch-translocation-of-masses-1942.pdf
I do not understand how he constructs the potential $U$ in the Necessity of the Condition part (p.3-4). Is $x_0$ supposed to $\zeta_n$ instead of $\zeta_0$? What is $y_0$ in the chain? And why is the expression $U(y)=r(x_0,y_0)-r(x_n,y_n)$ independent of the choice of the chain?