3 problems

Boundary correspondence conjecture. The correspondence between the ideal boundary and the space boundary of polygonal surfaces is the same as in Barbot surfaces.

Let $C_0$ be the standard cylinder, let $O_\theta\subset C_0$ be the obstacle obtained by rotating a fixed rectangular obstacle through angle $\theta$, and let…

Let $P$ be an arithmetic polygonal surface, let $G_\theta^t$ denote its directional flow, and call a direction $\theta$ rational or irrational as defined via a square-tiled model o…