Differentiability of monotone maps related to non-quadratic costs

Cristian E. Gutiérrez, Annamaria Montanari

The cost functions considered are $c(x,y)=h(x-y)$, with $h\in C^2(R^n)$, homogeneous of degree $p\ge 2$, with positive definite Hessian in the unit sphere. We consider monotone ma…