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...

We study connected orientable spacelike hypersurfaces $x:M^{n}rightarrowM_q^{n+1}(c)$, isometrically immersed into the Riemannian or Lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~L_kx=Ax+b$,~ where $L_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $H_{k+1}$ of the hypersurface for a fixed integer $0leq k

Numerical relativity describes a discrete initial value problem for general relativ-ity. A choice of gauge involves slicing space-time into space-like hypersurfaces. This introduces past and future gauge relative to the hypersurface of present time. Here, we propose solving the discretized Einstein equations with a choice of gauge in the future and a dynamical gauge in the past. The method is i...

The main idea of the support vector machine (SVM) classification approach is mapping the data into higher-dimensional linear space where the data can be separated by hyperplane. Based on the Jordan curve theory, a general nonlinear classification method by the use of hypersurface is proposed in this paper. The separating hypersurface is directly used to classify the data according to whether th...

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...

We consider radial solutions of a mass supercritical monic NLS and we prove the existence of a set, which looks like a hypersurface, in the space of finite energy functions, invariant for the flow and formed by solutions which converge to ground states. §

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...

We derive a general integral formula on an embedded hypersurface for general relativistic space-times. Suppose the hypersurface is foliated by two-dimensional compact “sections” Ss. Then the formula relates the rate of change of the divergence of outgoing light rays integrated over Ss under change of section to geometric (convexity and curvature) properties of Ss and the energy-momentum content...

When n satisfies an inequality which is almost best possible, we prove that the k-plane sections of every smooth, degree d, complex hypersurface in Pn dominate the moduli space of degree d hypersurfaces in Pk. As a corollary we prove that, for n sufficiently large, every smooth, degree d hypersurface in Pn satisfies a version of “rational simple connectedness”. 1. Statement of results In their ...