19 problems

Let $X^n$ be a compact complex manifold with $K_X$ nef and big, and let $tilde\omega(s)$ be the solution of the Chern-Ricci flow … starting at an arbitrary Hermitian metric…

Let $f:M\to\Sigma$ be an elliptic bundle over a Riemann surface $\Sigma$ of genus at least $2$, and let $\omega(t)$ solve the Chern-Ricci flow on $M$ from an arbitrary Gauduchon me…

Let $X$ be a classical Hopf surface, and consider the Chern--Ricci flow starting from the standard metric. The flow collapses in finite time and converges to a metric space in the…

Consider the Chern–Ricci flow on a classical Hopf surface, and suppose its Gromov–Hausdorff limit exists after the relevant collapsing and normalization. Round-circle conjecture. T…

Let $M$ be a Class VII$_0$ surface with $b_2(M)\geqslant1$, and let the Chern-Ricci flow develop its finite singular time $T$. Suppose that as $t\to T$, the metrics converge smooth…

Let $M$ be any Inoue surface. Let $\omega(t)$ be the Chern-Ricci flow and let $\omega_\infty$ be the closed semipositive $(1,1)$-form representing a multiple of $c_1(K_M)$ describe…

Let $M_{\alpha,\beta}$ be a Hopf surface, and let $\omega(t)$ be its Chern-Ricci flow, which for the standard Hopf metric collapses in the Gromov-Hausdorff sense to a circle as the…

In the setting of a general Kähler minimal properly elliptic surface $f:M\to\Sigma$, let $S$ be the union of the singular and multiple fibers, let $\omega(t)$ be the Chern-Ricci fl…

Let $f:M\to\Sigma$ be a general Kähler minimal properly elliptic surface, with singular and multiple fibers contained in $S$, and let $\omega(t)$ solve the Chern-Ricci flow from an…

Let $M^n$ be a compact complex manifold with nef canonical bundle $K_M$ and Kodaira dimension $\mathrm{Kod}(M)=n$. Let $\omega(t)$ solve the Chern-Ricci flow starting at an arbitra…

Let $S$ be an Inoue–Bombieri surface, let $\omega$ be a Gauduchon metric on $S$ (or more generally a Hermitian metric satisfying the obstruction condition), and let $\omega(t)$ be…

Let the Chern–Ricci flow be a solution on a primary Hopf surface constructed from a Gauduchon–Ornea locally conformally Kähler metric. The solutions reach a volume-collapsing singu…

Tosatti–Weinkove's continuation conjecture. The flow blows down the exceptional curves and continues in a unique way on the new surface $N$.

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 $\omega(t)$ be the solution of the Chern-Ricci flow on an Inoue surface, and let $\omega_\infty$ be the limiting metric in Theorem 1.1. Conjecture. The convergence of…

Let $\omega(t)$ be the solution of the Chern-Ricci flow on an Inoue surface with initial Hermitian metric $\omega_0$, and let $\omega_\infty$ denote the limiting metric appearing i…

Let $alpha=(\alpha_1,\ldots,\alpha_n)\in\mathbb{C}^n\setminus\{0\}$ satisfy $|\alpha_1|=\cdots=|\alpha_n|\ne1$, and let $M_\alpha=(\mathbb{C}^n\setminus\{0\})/\sim$ be the Hopf man…

Let $M$ be a compact complex surface with a $partial \overline{\partial}$-closed Hermitian metric, and suppose the Chern-Ricci flow reaches the finite-time situation in which $M$ c…

Let $M$ be a complex surface with a $partial \overline{\partial}$-closed metric. The Chern-Ricci flow starting from this metric is expected to exhibit behavior analogous to the Käh…