Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Penrose Inequality   In 1973, R. Penrose presented an argument that the total mass of a space-time
which contains black holes with event horizons of total area $A$ should be at
least $\sqrt{A/16\pi}$. An important special case of this physical statement
translates into a very beautiful mathematical inequality in Riemannian geometry
known as the Riemannian Penrose inequality. This inequality was first
established by G. Huisken and T. Ilmanen in 1997 for a single black hole and
then by one of the authors (H.B.) in 1999 for any number of black holes. The
two approaches use two different geometric flow techniques and are described
here. We further present some background material concerning the problem at
hand, discuss some applications of Penrose-type inequalities, as well as the
open questions remaining.

7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an