Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global Newlander-Nirenberg theorem for domains with $C^2$ boundary   The Newlander-Nirenberg theorem says that a formally integrable complex
structure is locally equivalent to the standard complex structure in the
complex Euclidean space. In this paper, we consider two natural generalizations
of the Newlander-Nirenberg theorem under the presence of a $C^2$ strictly
pseudoconvex boundary. When a given formally integrable complex structure $X$
is defined on the closure of a bounded strictly pseudoconvex domain with $C^2$
boundary $D\subset \mathbb{C}^n$, we show the existence of global holomorphic
coordinate systems defined on $\overline{D}$ that transform $X$ into the
standard complex structure provided that $X$ is sufficiently close to the
standard complex structure. Moreover, we show that such closeness is stable
under a small $C^2$ perturbation of $\partial D$. As a consequence, when a
given formally integrable complex structure is defined on a one-sided
neighborhood of some point in a $C^2$ real hypersurface $M\subset
\mathbb{C}^n$, we prove the existence of local one-sided holomorphic coordinate
systems provided that $M$ is strictly pseudoconvex with respect to the given
complex structure. We also obtain results when the structures are finite
smooth.

31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph