The concept of time is discussed in the context of the canonical formulation of the gravitational field. Using a hypersurface orthogonal foliation, the arbitrariness of the lapse function is eliminated and the shift vector vanishes, allowing a consistent definition of time. I. ON LAPSES AND SHIFTS As it well know, the space-time of Newtonian mechanics is foliated by globally defined 3-dimension...

We address the asymptotic behavior of ?-Gauss curvature flow, for ?>1/2, with a complete non-compact convex initial hypersurface which is contained in cylinder bounded cross section. show that flow converges, as t?+?, locally smoothly to translating soliton uniquely determined by hypersurface.

A geometrical characterization of robustly separable (that is, remaining separable under sufficiently small variiations) mixed states of a bipartite quantum system is given. It is shown that the density matrix of any such state can be represented as a normal vector to a hypersurface in the Euclidean space of all self-adjoint operators in the state space of the whole system. The expression for t...

A method for computing the open string mirror map and superpotential, using an extended set of PicardFuchs equations, is presented. This is based on techniques used by Lerche, Mayr and Warner in [4], [1]. For X a toric hypersurface and Y a hypersurface in X, the mirror map and superpotential are written down explicitly. As an example, the case of KP2 is worked out and shown to agree with the li...

We present our recent understanding on resolutions of Gorenstein orbifolds, which involves the finite group representation theory. We concern only the quotient singularity of hypersurface type. The abelian group Ar (n) for A-type hypersurface quotient singularity of dimension n is introduced. For n = 4, the structure of Hilbert scheme of group orbits and crepant resolutions of Ar (4)-singularit...

A topological interpretation of Hochster’s Theta pairing of two modules on a hypersurface ring is given in terms of linking numbers. This generalizes results of M. Hochster and proves a conjecture of J. Steenbrink. As a corollary we get that the Theta pairing vanishes for isolated hypersurface singularities in an odd number of variables, as was conjectured by H. Dao. 2000 Math. Subj. Class. 32S...

Taking the triangle areas as independent variables in the theory of Regge calculus can lead to ambiguities in the edge lengths, which can be interpreted as discontinuities in the metric. We construct solutions to area Regge calculus using a triangulated lattice and find that on a spacelike hypersurface no such discontinuity can arise. On a null hypersurface however, we can have such a situation...