4 problems

Completely monotone conjecture. The function $t\longmapsto I(X,t)$ is completely monotonous, that is

Let $T_t:\mathbb{C}\to\mathbb{C}$ be the deterministic transport maps associated with the hydrodynamic limit, let $t_{\mathrm{sing}}$ be the first singular time, and let $z_j(t)$ d…

Let $\nu$ be a rotationally invariant probability measure on $\mathbb{C}\backslash\{0\}$ satisfying $\int_{0}^{\varepsilon} \nu(\{|z| < r\})r^{-1}\,\operatorname{d}r<\infty$ for so…

Heat-flow coincidence conjecture. The heat flow semigroup $(T_t)$ defined by the paper's formula for $F:=P_{(D)}$ coincides with the heat flow constructed by Sturm.