The boundary-image conjecture for Poincaré–Einstein metrics
Boundary-image conjecture. For any component E0{\mathcal E}_{0}E0 of E{\mathcal E}E, Πˉ(∂E0)\bar{\Pi}(\partial {\mathcal E}_{0})Πˉ(∂E0) has empty interior in C{\mathcal C}C.