5 problems

The paper studies the Wasserstein gradient flow of the Sinkhorn divergence toward a target Gaussian measure, with a Gaussian source measure, and seeks a convergence criterion for t…

Zero-bandwidth limit conjecture. In this limit, the kernelized Wasserstein gradient-flow equation

Equality conjecture. Equality holds in the slope-control inequality, that is,

Let ${\mathcal{E}}$ be the entropy energy on the Wasserstein space of probability measures and let ${\mathcal{D}}$ be its dissipation functional. The local slope…

Let $\hat{\bm v}$ be the minimizer in the steepest descent direction problem \. The geometric tangent-space conjecture. The minimizer $\hat{\bm v}$ is always contained in the geo…