N ov 2 00 1 Hyperbolic theories of dissipation : Why and when do we need them ?

ar X iv : m at h / 06 11 50 4 v 1 [ m at h . G T ] 1 6 N ov 2 00 6 QUANTUM HYPERBOLIC GEOMETRY

We construct a new family, indexed by the odd integers N ≥ 1, of (2 + 1)-dimensional quantum field theories called quantum hyperbolic field theories (QHFT), and we study its main structural properties. The QHFT are defined for (marked) (2 + 1)-bordisms supported by compact oriented 3-manifolds Y with a properly embedded framed tangle LF and an arbitrary PSL(2,C)character ρ of Y \LF (covering, f...

ar X iv : h ep - p h / 02 11 19 2 v 1 1 3 N ov 2 00 2 Why We Need Both the LHC and an e + e − Linear Collider ⋆

Why Hyperbolic Theories of Dissipation Cannot Be Ignored: Comments on a Paper by Kostädt and Liu

Contrary to what is asserted in a recent paper by Kostädt and Liu (“Causality and stability of the relativistic diffusion equation”) [1], experiments can tell apart (and in fact do) hyperbolic theories from parabolic theories of dissipation. It is stressed that the existence of a non–negligible relaxation time does not imply for the system to be out of the hydrodynamic regime. Also at UCV, Cara...

N ov 2 00 6 A Combination Theorem for Strong Relative Hyperbolicity Mahan

We prove a combination theorem for trees of (strongly) relatively hyperbolic spaces and finite graphs of (strongly) relatively hyperbolic groups. This gives a geometric extension of Bestvina and Feighn's Combination Theorem for hyperbolic groups.

ar X iv : h ep - t h / 03 09 13 9 v 2 9 N ov 2 00 3 1 Inflation from String / M - Theory Compactification ? ∗

We present some exact scalar potentials for the dimensionally reduced theory and examine the possibility of obtaining accelerating 4d cosmology from String/M-theory, more generally, hyperbolic and flux compactification. In the hyperbolic case, even in the zero-flux limit, the scalar potential is positive for the 4d effective theory as required to get an accelerating universe, and thereby evadin...