论文标题
在最佳运输中以非二次成本产生的单调图的精细特性
Fine properties of monotone maps arising in optimal transport for non-quadratic costs
论文作者
论文摘要
所考虑的成本功能为$ c（x，y）= h（x-y）$，其中$ h \ in c^2（\ mathbb {r}^n）$，均值$ p \ geq 2 $，在单位球体中具有正确定的hessian。我们研究了有关该成本的多晕单片图，并确定它们几乎在任何地方都具有单一的价值。然后推导进一步的后果。
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.
