2 problems

Relative unique-ergodicity conjecture. There is a neighborhood $\mathcal{U}$ of $0$ in $\mathrm{REL}$ such that $\mathbf{a}+\mathcal{U}\subset\mathbb{R}^d_+$ and…

The lines-and-curves conjecture. (Lines) If $\mathbf{a}$ is uniquely ergodic and $\ell$ is a line in $\mathbb{R}^d_+$ passing through $\mathbf{a}$, then there is a neighborhood…