Holomorphic maps with large images · arXivDeskAbstract
We show that each pseudoconvex domain Ω⊂Cn admits a holomorphic map F to Cm with ∣F∣≤C1eC2δ^−6
, where
is the minimum of the boundary distance and
(1+∣z∣2)−1/2 , such that every boundary point is a Casorati-Weierstrass point of
. Based on this fact, we introduce a new anti-hyperbolic concept --- universal dominability. We also show that for each
and each pseudoconvex domain
Ω⊂Cn , there is a holomorphic function
on
with
∣f∣≤CαeCα′δ^−α , such that every boundary point is a Picard point of
. Applications to the construction of holomorphic maps of a given domain onto some
are given.