Compactness theorems for sequences of pseudo-holomorphic coverings between domains in almost complex manifolds
Ourimi, Nabil . 2017
Our aim in this paper is to characterize smooth domains $(D, J)$
and $(D',J')$ in almost complex manifolds of real dimension $2n+2$
with a covering orbit $\{f_k (p)\}$, accumulating at a strongly
pseudoconvex boundary point, for some $(J,J')$-holomorphic
coverings $f_k : (D,J)\rightarrow (D', J')$ and $p\in D$. It was
shown that such domains are both biholomorphic to a model domain,
if the source domain $(D,J)$ admits a bounded strongly
$J$-plurisubharmonic exhaustion function. Furthermore, if the
target domain $(D',J')$ is strongly pseudoconvex, then both $(D,
J)$ and $(D',J')$ are biholomorphic to the unit ball in ${\mathbb
C}^{n+1}$ with the standard complex structure. Our results can be
considered as compactness theorems for sequences of
pseudo-holomorphic coverings. They generalize \cite{LW} and
\cite{Ourimi1} for relatively compact domains in almost complex
manifolds.
For any ${\mathcal C}^{\infty}$-smooth almost complex structure $J'$ on ${\mathbb C}^{n+1},$ we prove that any proper holomorphic mapping from a model domain in ${\mathbb C}^{n+1}$ to a bounded…
Our aim in this paper is to characterize smooth domains $(D, J)$
and $(D',J')$ in almost complex manifolds of real dimension $2n+2$
with a covering orbit $\{f_k (p)\}$, accumulating…
Let D, D be arbitrary domains in Cn and CN respectively, 1 < n < N, both possibly
unbounded and let M ⊂ ∂D, M'⊂ ∂D' be open pieces of the boundaries. Suppose that ∂D
is smooth real-…