3 problems

Let $(M^n,\omega_M)$ be a compact Hermitian manifold of complex dimension $n$, with fixed Hermitian metric $\omega_M$, and let $F\in C^\infty(M,\mathbb{R})$ be a smooth real functi…

Dinh–Nguyen–Sibony conjecture. If $\mu$ is moderate, then its Monge–Ampère potential $u$ is Hölder continuous; equivalently, the functional

Geometric subsolution conjecture. There exists a $k$-positive form $'\text{ in }[]$ satisfying the inequality from the paper with $'$ in place of …