Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence, Regularity, and Properties of Generalized Apparent Horizons   We prove a conjecture of Tom Ilmanen's and Hubert Bray's regarding the
existence of the outermost generalized apparent horizon in an initial data set
and that it is outer area minimizing.

6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics