Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How do difference bodies in complex vector spaces look like? A
  geometrical approach   We investigate geometrical properties and inequalities satisfied by the
complex difference body, in the sense of studying which of the classical ones
for the difference body have an analog in the complex framework. Among others
we give an equivalent expression for the support function of the complex
difference body and prove that, unlike the classical case, the dimension of the
complex difference body depends on the position of the body with respect to the
complex structure of the vector space. We use spherical harmonics to
characterize the bodies for which the complex difference body is a ball, we
prove that it is a polytope if and only if the two bodies involved in the
construction are polytopes and provide several inequalities for classical
magnitudes of the complex difference body, as volume, quermassintegrals and
diameter, in terms of the corresponding ones for the involved bodies.

17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci