Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schwarzian derivatives for pluriharmonic mappings   A pre-Schwarzian and a Schwarzian derivative for locally univalent
pluriharmonic mappings in ${\mathbb C}^n$ are introduced. Basic properties such
as the chain rule, multiplicative invariance and affine invariance are proved
for these operators. It is shown that the pre-Schwarzian is stable only with
respect to rotations of the identity. A characterization is given for the case
when the pre-Schwarzian derivative is holomorphic. Furthermore, it is shown
that if the Schwarzian derivative of a pluriharmonic mapping vanishes then the
analytic part of this mapping is a M\"obius transformation.
  Some observations are made related to the dilatation of pluriharmonic
mappings and to the dilatation of their affine transformations, revealing
differences between the theories in the plane and in higher dimensions. An
example is given that rules out the possibility for a shear construction
theorem to hold in ${\mathbb C}^n$, for $n\geq2$.

8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg