8 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…

Strict rescaling quotient conjecture. One has

Let $\Omega$ be the domain under consideration, let $\varphi$ be the prescribed singularity type, and let $\mathcal{E}(\Omega)\subseteq\mathcal{D}(\Omega)$ denote the relevant clas…

Let $\Omega$ be a smoothly bounded strictly pseudoconvex Reinhardt domain in $\mathbb C^n$, let $M=\{z\in\mathbb C^n\mid z_1\cdots z_n=0\}$, and let $\phi$ be a weak geodesic solvi…

Let $u_\sigma$ be the solution on the Tian–Yau region $\mathfrak{R}_7$ arising in the construction of the negative Kähler–Einstein metric, and let $b$ be the gluing parameter. For…

Let $(M,\omega)$ be a compact Hermitian manifold, and let $F$ be the prescribed right-hand side in the complex Monge–Ampère equation. A Hermitian metric of the form … represents a…

Tosatti–Weinkove's canonical surgical contraction conjecture. There exists a smooth maximal solution $\omega_t$ of the Chern–Ricci flow on $Y$ for $t\in(T,T_Y)$, with…

Let $\mathcal{B}\subset\mathbb{C}^{n}$ be the ball, and consider the equation referred to in the source as equation, with parameter $\gamma$. Let $u_{\gamma}$ denote the radial sol…