3 problems

Savini's boundary-map conjecture. Given a Zariski-dense measurable cocycle $\sigma:\Gamma\times X\rightarrow G$, the cocycle has a boundary map.

Corner-point conjecture. The corner points of $\Omega_{\overline{A}}$ for extremal $\overline{A}$ should be of the form $(\cdot,Q_i)$ for lower corners and $(\cdot,P_i)$ for upper…

Let $\mathfrak{g}_0=\langle e,f,h\rangle\subset\mathfrak{g}$ be a three-dimensional simple Lie algebra, with $e$ the nilpotent element, and suppose … The corresponding totally geod…