7 problems

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 $S$ 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 $(M^4,J)$ be an Inoue surface, and let $\omega_0$ be a pluriclosed metric on $M$. Inoue surface geometrization conjecture. The solution $\omega_t$ to pluriclosed flow with this…

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…

Nonexistence conjecture. Inoue surfaces of type $S^0$ do not admit para-hyperhermitian structures at all.

Let $X$ be a non-elliptic compact complex surface admitting a positive, multiplicatively automorphic, non-constant, pluriharmonic function on a ${\mathbb Z}$-covering. Inoue-surfac…