4 problems

Let $\phi:[0,1]\rightarrow [0,1]$ be an $\alpha$-Hölder continuous map for some $\alpha\in(0,1)$. The metric mean dimension…

Let $\phi:[0,1]\rightarrow [0,1]$ be an $\alpha$-Hölder continuous map, with $\alpha>0$. The metric mean dimension $\operatorname{mdim}_{\operatorname{M}}([0,1],|\cdot|,\phi)$ is t…

Let $\phi:[0,1]\rightarrow [0,1]$ be an $\alpha$-Hölder continuous map. The metric mean dimension $\operatorname{mdim}_{\operatorname{M}}([0,1],|\cdot|,\phi)$ is defined using the…

The uniqueness conjecture. Such a solution $u(t)$ cannot possess another solution $v(t)$ satisfying these initial conditions.