Found via Exporting the past into the future, or, "The Possibility Jelly lives on the hypersurface of the present" which in turn came via a tweet. ❋ Mia (2009)
Now, in an open or flat Friedmann-Robertson-Walker cosmological model with no cosmological constant, whilst the past 'Big-Bang' singularity corresponds to a spacelike hypersurface in the boundary of the conformal compactification, the future timelike infinity corresponds to a single point. ❋ Gordon McCabe (2009)
The far future of our universe is therefore representable by de Sitter space-time, and in this type of space-time the future timelike boundary is a spacelike hypersurface. ❋ Gordon McCabe (2009)
The Weyl curvature is zero on both the future boundary and past boundary, hence the Big Bang is still well-defined in the cyclic model as the unique hypersurface on which the Weyl curvature vanishes. ❋ Gordon McCabe (2009)
Given an initial condition on a time-like hypersurface as a mathematical model for the universe, we can determine in which direction a dynamics (supposed here to be deterministic, whether applied to a quantum or to a classical state) causes the entropy to increase or to decrease. ❋ Sean (2007)
Oh and BTW, the mind is a maximum hypersurface and thought a trajectory on it and the amygdala and hippocampus are Hopf maps of it. ❋ Unknown (2006)
On the monodromy theorem for isolated hypersurface singularities. ❋ Unknown (2006)
The shock waves the hypersphere gave off were only "sound" along one surface (hypersurface?) of the concentrically expanding ripples of pressure. ❋ Unknown (2005)
There are only six points on the hypersurface where the axis intersects it that form three-spheres. ❋ Unknown (2005)
S** is moving so fast with respect to the tachyon source that the hypersurface becomes titled so much that the arrow points into the past below the hypersurface. ❋ Faye, Jan (2005)
An observer in S* observes the tachyon to have infinite speed, and therefore the hypersurface is tilted so much that it coincides with the arrow. ❋ Faye, Jan (2005)
S, and the arrow of trajectory is for that reason pointing into the future above the hypersurface passing through A and standing perpendicular to the world-line of the source. ❋ Faye, Jan (2005)
M is a spacelike hypersurface, there does not exist a spacetime ❋ Earman, John (2004)
This situation can arise because of a poor choice of initial value hypersurface, as illustrated in ❋ Earman, John (2004)
We make this third condition precise by requiring that the spacetime admits a global time slice Σ (i.e., a spacelike hypersurface without edges); [9] that Σ is two-sided and partitions ❋ Earman, John (2004)
According to an editorial footnote in the collection of his scientific papers (WA I, 96), Boltzmann's personal copy of the paper contains a hand-written remark in the margin stating that the point was still dubious and that it had not been proven that, even including interaction with an external atom, the trajectory would traverse all points on the energy hypersurface. ❋ Uffink, Jos (2004)
This trajectory is constrained to lie on a given energy hypersurface ❋ Uffink, Jos (2004)
