Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: BV spaces and the perimeters related to Schrodinger operators with
  inverse-square potentials and applications to the rank-one theorem   For $a \ge - {( \frac{{d}}{2}- 1)^2} $ and $2\sigma= {{d - 2}}-( {{{(d -
2)}^2} + 4a})^{1/2}$, let $$\begin{cases}\mathcal{H}_{a}= - \Delta + \frac{a}
{{{{ | x |}^2}}},\\ \mathcal{\widetilde{H}}_{\sigma}= 2\big( { - \Delta +
\frac{{{\sigma ^2}}} {{{{ | x |}^2}}}}\big)\end{cases}$$ be two Schr\"odinger
operators with inverse-square potentials. In this paper, on the domain $\Omega
\subset {\mathbb {R}^d}\backslash \{ 0\}, d\geq 2,$ %apart from the origin, the
${\mathcal{H} _a}$-BV space $\mathcal{B} {\mathcal{V} _{{\mathcal{H}
_a}}}(\Omega )$ and the ${\mathcal{\widetilde{H}}_{\sigma}}$-BV space
$\mathcal{B} {\mathcal{V} _{{\mathcal{\widetilde H} _\sigma}}}(\Omega )$
related to $\mathcal{H}_{a}$ and $\mathcal{\widetilde{H}}_{\sigma}$ are
introduced, respectively. We investigate a series of basic properties of
$\mathcal{B} {\mathcal{V} _{{\mathcal{H} _a}}}(\Omega )$ and $\mathcal{B}
{\mathcal{V} _{{\mathcal{\widetilde H} _{\sigma}}}}(\Omega )$. Furthermore, we
prove that ${\mathcal{\widetilde{H}}_{\sigma}}$-restricted BV functions can be
characterized equivalently via their subgraphs. As applications, we derive the
rank-one theorem for ${\mathcal{\widetilde{H}}_{\sigma}}$-restricted BV
functions.

29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn