9 problems

Boundary-case J-flow convergence conjecture. In this boundary case, the J-flow converges to a critical metric on compact subsets of $M\setminus S$. This conjecture concerns the bor…

Let $(M,\theta)$ be a compact Kähler manifold of complex dimension $n$, let $\theta$ be a Kähler metric, and let $[\chi]$ be a Kähler cohomology class represented by a Kähler metri…

Conjectured equivalence. The two conditions—existence of a J-balanced metric and Chow stability of $|L_2|$—should be equivalent.

Transition-map compactness conjecture. The derivative $DU_t$ should remain uniformly bounded with respect to time, and $U_t$ should converge to a limit map $U_\infty$ even when the…

Donaldson's blow-up conjecture. If this condition is violated, then the J-flow should blow up over curves with negative self-intersection. The source states that in complex dimensi…

Lejmi–Székelyhidi's conjecture. These inequalities should be sufficient for the Donaldson equation to have a solution. The inequalities depend only on the cohomology classes…

Let $M$ be an $n$-dimensional compact Kähler manifold, let $\alpha$ be a fixed Kähler metric, and let $\omega$ vary in a fixed Kähler class. For $k=1,\ldots,n$, define the inverse…

Let $(M,\omega)$ be a compact Kähler manifold, let $\alpha$ be a second Kähler metric, and let $c$ be the constant determined by the Kähler classes through … The J-flow is the evol…

Let $(M,\omega)$ be a compact Kähler manifold of dimension $n$, let $\alpha$ be a second Kähler metric on $M$, and let $c$ be determined by … For a $p$-dimensional subvariety…