11 problems

Let $M$ be a compact Einstein contact metric manifold. Contact Goldberg conjecture. $M$ is Sasakian–Einstein. This is proposed as the contact-metric analogue of the Goldberg conjec…

Let $(X,L)$ be a polarized smooth projective variety with $\mathbb{T}$, $\mathfrak{t}_+$, $\mathcal{EH}$, $\mathcal{Y}_{\mathrm{sup}}$, and the three conditions of Proposition as i…

Let $M^3_g(n) \star_{\ell_1,\ell_2} S^3_{\mathbf w}$ be a Sasaki join, where $g$ is the genus of a surface $\Sigma_g$, $n$ is the Euler class of a circle bundle over $\Sigma_g$,…

Analytic log minimal model conjecture. There should be a Sasaki analogue of the analytic log minimal model program with respect to $K_Z+[\Delta]$, realized via the conical Sasaki-R…

Analytic log minimal model conjecture. There is a Sasaki analogue of the analytic log minimal model program with respect to $K_Z+[\Delta]$ via the conical Sasaki-Ricci flow.

Let $M_K$ be the fiber join constructed from the positive line bundles $L_1$ and $L_2$ over ${\mathbb C}{\mathbb P}^1\times{\mathbb C}{\mathbb P}^1$, and let…

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…

The sixth example consists of families of rational homology spheres of dimension $4n-1$ with $H_{2n}\approx \mathbb{Z}_3$, including links $K_{6l+2}$ and $K_{6l+4}$ related to…

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…