Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral theory, Hausdorff dimension and the topology of hyperbolic
  3-manifolds   Let M be a compact 3-manifold whose interior admits a complete hyperbolic
structure. We let Lambda(M) be the supremum of the bottom eigenvalue of the
Laplacian of N, where N varies over all hyperbolic 3-manifolds homeomorphic to
the interior of M. Similarly, we let D(M) be the infimum of the Hausdorff
dimensions of limit sets of Kleinian groups whose quotients are homeomorphic to
the interior of M. We observe that Lambda(M)=D(M)(2-D(M)) if M is not
handlebody or a thickened torus. We characterize exactly when Lambda(M)=1 and
D(M)=1 in terms of the characteristic submanifold of the incompressible core of
M.

15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an