论文标题
最佳分号的奇异性拓扑
Topology of Singularities of Optimal Semicouplings
论文作者
论文摘要
我们研究了$ c $ - 最佳的半偶联的奇异性拓扑。我们的主要结果描述了从源空间$（x，σ）$ $ z_j $，$ j \ geq 0 $ of $ c $ -c $ - optimemal optimal ematimal neve $（y，τ）$是riemannian目标空间，而$ c $的成本是$ x \ x y $ x y $ c $，$ x $ c $是$ x $ y $ c $，我们构建连续的强变形缩回$ x \ ledssto z_j $，每当沿适当子集满足称为统一半空（UHS）条件的条件时。本文总结了作者博士学位论文（2019）的一些结果。
We study the topology of singularities of $c$-optimal semicouplings in unequal dimension. Our main results describe homotopy-reductions from a source space $(X,σ)$ onto the singularities $Z_j$, $j\geq 0$ of $c$-optimal semicouplings whenever $(Y, τ)$ is a Riemannian target space and $c$ is a cost on $X\times Y$ satisfying some general assumptions (A0)--(A5). We construct continuous strong deformation retracts $X\leadsto Z_j$ whenever a condition called Uniform Halfspace (UHS) condition is satisfied along appropriate subsets. This article summarizes some results from the author's PhD thesis (2019).
