  The cost functions considered are $c(x,y)=h(x-y)$, where $h\in
C^2(\mathbb{R}^n)$, homogeneous of degree $p\geq 2$, with a positive definite
Hessian in the unit sphere. We study multivalued monotone maps with respect to
that cost and establish that they are single-valued almost everywhere. Further
consequences are then deduced.
