3 problems

Relative K-stability conjecture. The existence of an extremal metric is conjectured to be equivalent to relative K-stability.

Donald's relative K-polystability conjecture. If $(Q_i,d\sigma_i)$ is relatively K-polystable, then there exists a complete extremal metric on $V_{Q_i}\setminus D_i$.

Relative K-polystability conjecture for pairs. $(V,D,L)$ is relatively K-polystable with a positive modulus of stability if and only if there exists a complete extremal metric on…