4 problems

Let $f:X\to X$ be a holomorphic or meromorphic self-map of a compact complex manifold $X$, inducing actions $f^*,f_*:H^*(X,\mathbb{R})\to H^*(X,\mathbb{R})$ on the real cohomology…

Let $X$ be a Zariski open subset of an irreducible compact complex space. A compact irreducible complex space $Y$ is hyperbolic in the sense used by Noguchi, and $f:X\rightarrow Y$…

Let $X$ be a compact Kähler manifold of dimension $m$, and let $f:X\dashrightarrow X$ be a dominant meromorphic map. The map $f$ is cohomologically hyperbolic if one dynamical degr…

Extension property. Every non-degenerate holomorphic map