Analytic sets extending the graphs of holomorphic mappings between domains of different dimensions.
OURIMI, Maryiam Al Towaileb- NABIL . 2012
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-analytic and minimal in an open neighborhood of ¯M and ∂D is smooth realalgebraic
and minimal in an open neighborhood of ¯M. Let f : D → D be a holomorphic
mapping. Assume that the cluster set cl f (M) does not intersect D. It is proved that if the
cluster set cl f (p) of a point p ∈ M contains some point q ∈ M and the graph of f extends
as an analytic set to a neighborhood of (p, q) ∈ Cn ×CN, then f extends as a holomorphic
map near p.
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-…