Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isoperimetry of waists and local versus global asymptotic convex
  geometries   Existence of nicely bounded sections of two symmetric convex bodies K and L
implies that the intersection of random rotations of K and L is nicely bounded.
For L = subspace, this main result immediately yields the unexpected
phenomenon: "If K has one nicely bounded section, then most sections of K are
nicely bounded". This 'existence implies randomness' consequence was proved
independently in [Giannopoulos, Milman and Tsolomitis]. The main result
represents a new connection between the local asymptotic convex geometry (study
of sections of convex bodies) and the global asymptotic convex geometry (study
of convex bodies as a whole). The method relies on the new 'isoperimetry of
waists' on the sphere due to Gromov.

29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom