The existence of closed hypersurfaces of prescribed scalar curvature in globally hyperbolic Lorentzian manifolds is proved provided there are barriers. 0. Introduction Consider the problem of finding a closed hypersurface of prescribed curvature F in a globally hyperbolic (n+1)-dimensional Lorentzian manifold N having a compact Cauchy hypersurface S0. To be more precise, let Ω be a connected op...

1480 NOTICES OF THE AMS VOLUME 42, NUMBER 12 T he theory of functions (what we now call the theory of functions of a complex variable) was one of the great achievements of nineteenth century mathematics. Its beauty and range of applications were immense and immediate. The desire to generalize to higher dimensions must have been correspondingly irresistible. In this desire to generalize, there w...

We investigate freeze–out in hydrodynamic models for relativistic heavy–ion collisions. In particular, instantaneous freeze–out across a hypersurface of constant temperature (“isothermal” freeze–out) is compared with that across a hypersurface at constant time in the center-of-momentum frame (“isochronous” freeze–out). For one– dimensional (longitudinal) expansion the rapidity distributions are...

We formulate the basic postulate of pre-big bang cosmology as one of “asymptotic past triviality”, by which we mean that the initial state is a generic perturbative solution of the tree-level low-energy effective action. Such a past-trivial “string vacuum” is made of an arbitrary ensemble of incoming gravitational and dilatonic waves, and is generically prone to gravitational instability, leadi...

A criterion for a spacelike hypersurface in a conformally stationary spacetime to be a Cauchy hypersurface is given. The criterion is based on the forward and the backward completeness of a non-reversible Finsler metric associated to the hypersurface.

We study the energy-momentum and baryonic number conservation laws for quark-gluon plasma discontinuity transitions into hadron matter states. We find that the time-like shock hadronization of a supercooled quark-gluon plasma (when the normal vector to the discontinuity hypersurface is timelike) should take place. We consider some properties of this process, which is different from the standard...

Eastwood and Ezhov generalized the Cayley surface to the Cayley hypersurface in each dimension, proved some characteristic properties of the Cayley hypersurface and conjectured that a homogeneous hypersurface in affine space satisfying these properties must be the Cayley hypersurface. We will prove this conjecture when the domain bounded by a graph of a function defined on Rn is also homogeneou...

The relativistic kinetic equations for the two domains separated by the hypersurface with both spaceand time-like parts are derived. The particle exchange between the domains separated by the time-like boundaries generates source terms and modifies the collision term of the kinetic equation. The correct hydrodynamic equations for the “hydro+cascade” models are obtained and their differences fro...