  We investigate a model of large extra dimensions where the internal space has
the geometry of a hyperbolic disc. Compared with the ADD model, this model
provides a more satisfactory solution to the hierarchy problem between the
electroweak scale and the Planck scale, and it also avoids constraints from
astrophysics. In general, a novel feature of this model is that the physical
results depend on the position of the brane in the internal space, and in
particular, the signal almost disappears completely if the brane is positioned
at the center of the disc. Since there is no known analytic form of the
Kaluza-Klein spectrum for our choice of geometry, we obtain a spectrum based on
a combination of approximations and numerical computations. We study the
possible signatures of our model for hadron colliders, especially the LHC,
where the most important processes are the production of a graviton together
with a hadronic jet or a photon. We find that the signals are similar to those
of the ADD model, regarding both qualitative behavior and strength. For the
case of hadronic jet production, it is possible to obtain relatively strong
signals, while for the case of photon production, this is much more difficult.
