Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hessian valuations   A new class of continuous valuations on the space of convex functions on
$\mathbb{R}^n$ is introduced. On smooth convex functions, they are defined for
$i=0,\dots,n$ by \begin{equation*} u\mapsto \int_{\mathbb{R}^n}
\zeta(u(x),x,\nabla u(x))\,[\operatorname{D}^2 u(x)]_i\,{\rm d} x
\end{equation*} where $\zeta\in
C(\mathbb{R}\times\mathbb{R}^n\times\mathbb{R}^n)$ and $[\operatorname{D}^2
u]_i$ is the $i$th elementary symmetric function of the eigenvalues of the
Hessian matrix, $\operatorname{D}^2 u$, of $u$. Under suitable assumptions on
$\zeta$, these valuations are shown to be invariant under translations and
rotations on convex and coercive functions.

4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
1
The categories of this paper are: cs