K-polystability and reduced uniform K-stability of log Fano cone singularities

Linsheng Wang

We prove that a log Fano cone $(X,\Delta ,{\xi }_0)$ satisfying ${\delta }_{\mathbb{T}}(X,\Delta ,{\xi }_0)\ge 1$ is K-polystable for normal test configurations if and only if it is K-polystable for special test…