Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizing circles by a convex combinatorial property   Let $K_0$ be a compact convex subset of the plane $\mathbb R^2$, and assume
that $K_1\subseteq \mathbb R^2$ is similar to $K_0$, that is, $K_1$ is the
image of $K_0$ with respect to a similarity transformation $\mathbb
R^2\to\mathbb R^2$. Kira Adaricheva and Madina Bolat have recently proved that
if $K_0$ is a disk and both $K_0$ and $K_1$ are included in a triangle with
vertices $A_0$, $A_1$, and $A_2$, then there exist a $j\in \{0,1,2\}$ and a
$k\in\{0,1\}$ such that $K_{1-k}$ is included in the convex hull of
$K_k\cup(\{A_0,A_1, A_2\}\setminus\{A_j\})$. Here we prove that this property
characterizes disks among compact convex subsets of the plane. Actually, we
prove even more since we replace "similar" by "isometric" (also called
"congruent"). Circles are the boundaries of disks, so our result also gives a
characterization of circles.

18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int