Monge-Ampère currents over pseudoconcave spaces

Uniformisation of Foliations by Curves

“…Extension of meromorphic maps. As in [Din,§6], we shall use the volume estimate of Theorem 7.1 to get an extension theorem for certain meromorphic maps into Kähler manifolds.…”

“…Therefore Ω = Γ f , and condition (A) of Theorem 7.1 is fulfilled. [Din,§4]. We just have to exhibit a ω-plurisubharmonic function on Γ f which is nonpositive on U and exhaustive on Γ f \ U .…”

“…Consider the open subset Ω ⊂ Γ f where the functions of P ω (Γ f , U ) are locally uniformly bounded from above. It contains U , and it is a general fact that it is locally pseudoconvex in Γ f [Din,§3].…”