Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rotation invariant Minkowski classes of convex bodies   A Minkowski class is a closed subset of the space of convex bodies in
Euclidean space Rn which is closed under Minkowski addition and non-negative
dilatations. A convex body in Rn is universal if the expansion of its support
function in spherical harmonics contains non-zero harmonics of all orders. If K
is universal, then a dense class of convex bodies M has the following property.
There exist convex bodies T1; T2 such that M + T1 = T2, and T1; T2 belong to
the rotation invariant Minkowski class generated by K. It is shown that every
convex body K which is not centrally symmetric has a linear image, arbitrarily
close to K, which is universal. A modified version of the result holds for
centrally symmetric convex bodies. In this way, a result of S. Alesker is
strengthened, and at the same time given a more elementary proof.

29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph