4 problems

Form-type Calabi–Yau equation solvability conjecture. There exist a constant $b$ and a function $\varphi$ satisfying these equations. The equation is introduced as the form-type Ca…

Let $M$ be a compact complex manifold with vanishing Bott–Chern first Chern class $c_1^{BC}=0$ and a balanced metric $\omega_0$. A Hermitian metric is balanced if…

Let $X$ be a compact complex manifold of dimension $n$ with holomorphic volume form $\Omega$. Let $\omega$ be a Hermitian metric satisfying … and denote its balanced class by…

The balanced Calabi–Yau metric conjecture. There is a balanced metric $\tilde{\omega}$ with