3 problems

Let $\nu_0$ and $\nu_1$ be endpoint measures, and let $\operatorname{UOT}^{\mathrm{D}}(\nu_0,\nu_1)$ be the diffusion-based unbalanced optimal transport functional defined by minim…

Strong duality conjecture. Strong duality also holds when $\boldsymbol{\sigma}$ is Lebesgue measure on $\mathbb{S}^{d-1}$.

MTW implication conjecture. The MTW condition for the cost on the cone should imply the MTW condition for the induced cost on the base manifold, possibly for costs other than the g…