Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Landis' conjecture in the plane   In this paper we prove a quantitative form of Landis' conjecture in the
plane. Precisely, let $W(z)$ be a measurable real vector-valued function and
$V(z)\ge 0$ be a real measurable scalar function, satisfying
$\|W\|_{L^{\infty}({\mathbf R}^2)}\le 1$ and $\|V\|_{L^{\infty}({\mathbf
R}^2)}\le 1$. Let $u$ be a real solution of $\Delta u-\nabla(Wu)-Vu=0$ in
${\mathbf R}^2$. Assume that $u(0)=1$ and $|u(z)|\le\exp(C_0|z|)$. Then $u$
satisfies $\underset{{|z_0|=R}}{\inf}\,\underset{|z-z_0|<1}{\sup}|u(z)|\ge
\exp(-CR\log R)$, where $C$ depends on $C_0$. In addition to the case of the
whole plane, we also establish a quantitative form of Landis' conjecture
defined in an exterior domain.

29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th