Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gromov hyperbolic John is quasihyperbolic John I   In this paper, we introduce a concept of quasihyperbolic John spaces and
provide a necessary and sufficient condition for a space to be quasihyperbolic
John. Using this criteria, we exhibit a simple proof to show that a John space
with a Gromov hyperbolic quasihyperbolization is quasihyperbolic John,
quantitatively. This answers affirmatively to an open question proposed by
Heinonen (Rev.~Math.~Iber, 1989), which was studied by Gehring et al.
(Math.~Scand, 1989). As a tool, we study its connection between several
geometric conditions.

37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio