4 problems

Extremal K-polystability conjecture. In the setting of Theorem, for any $\check{\mathbb T}$-equivariant smooth Kähler test configuration $({\mathscr M},{\mathscr A})$ associated to…

Let $(M,g)$ be a $(2n+1)$-dimensional Sasaki manifold with transverse Kähler form … Suppose that $M$ admits a transverse Sasaki–Einstein metric. Let $K$ be a maximal compact subgro…

Let $(M,\xi)$ be a Sasakian manifold polarized by the Reeb vector field $\xi$, with polarized affine cone $(Y,\xi)$, where $Y=C(M)$ is the fixed complex cone. A constant scalar cur…

Let $M$ be a compact co-oriented toric contact manifold of Reeb type. Let $\mathcal{C}$ be its strictly convex good cone, let $\mathcal{C}_+^*$ denote the Reeb cone, and for…