3 problems

Generalized barycentric projection conjecture. The map $cmathcal{T}_{cgamma^*}$ is a Monge mapping for the $coperatorname{GW}(cmathbb{S},ctilde{cmathbb{X}}_{cgamma^*})$ problem. Th…

Tightness conjecture. Theorem is tight: there exist $\mu$ and $\nu$ for which optimal correspondence plans for the quadratic Gromov–Wasserstein problem are not maps, but are instea…

Let $p\in[1,\infty)$, and let an $\ell^p$-Gromov-Wasserstein geodesic be a geodesic for the $\ell^p$-Gromov-Wasserstein distance. A geodesic is Hausdorff-bounded if it satisfies th…