Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infimum of the exponential volume growth and the bottom of the essential
  spectrum of the Laplacian   The purpose of this paper is to point out that `supremum' in two inequalities
of Brooks should be replaced with `infimum'.
  The results of this paper are already known by Professor Higuci. Hence, I
want to delete this paper from this preprint server.

14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom