Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric properties of the Cassinian metric   In this paper we prove a sharp distortion property of the Cassinian metric
under M\"obius transformations of a punctured ball onto another punctured ball.
The paper also deals with discussion on local convexity properties of the
Cassinian metric balls in some specific subdomains of $\mathbb{R}^n$. Inclusion
properties of the Cassinian metric balls with other hyperbolic-type metric
balls are also investigated. In particular, several conjectures are also stated
in response to sharpness of the inclusion relations.

25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio