Related papers: A compactification of outer space which is an abso…
The self-similar structure of the attracting subshift of a primitive substitution is carried over to the limit set of the repelling tree in the boundary of Outer Space of the corresponding irreducible outer automorphism of a free group.…
We prove pseudocompactness of a Tychonoff space $X$ and the space $\mathcal{P}(X)$ of Radon probability measures on it with the weak topology under the condition that the Stone-\v{C}ech compactification of the space $\mathcal{P}(X)$ is…
We study conformal theories of gravity, i.e. those whose action is invariant under the local transformation g_{\mu\nu} -> \omega^2 (x) g_{\mu\nu}. As is well known, in order to obtain Einstein gravity in 4D it is necessary to introduce a…
It is shown that the local coupling of a higher dimensional graviton to a closed degenerate two-form produces dimensional reduction by spontaneous breakdown of extra-dimensional translational symmetry. Four dimensional Poincar\'e invariance…
We study the compactification of nonautonomous systems with autonomous limits and related dynamics. Although the $C^{1}$ extension of the compactification was well established, a great number of problems arising in bifurcation and stability…
We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical lemma we need is a new manifestation of Akemann and…
We construct supergravity backgrounds representing non-homogeneous compactifications of d=10,11 supergravities to four dimensions, which cannot be written as a direct product. The geometries are regular and approach $AdS_7\times S^4$ or…
The cosmic vacuum is the wavefunction of the eleven dimensional Planck supermembrane. The Planck wavefunction is the superposition of dimensions from eleven to four dimensional spacetime with decreasing energy and increasing size. The…
We give a careful general relativistic and (1+3)-covariant analysis of cosmological peculiar velocities induced by matter density perturbations in the presence of a cosmological constant. In our quasi-Newtonian approach, constraint…
Exact Newtonian potential with an extra space dimension compactified on a circle is derived and studied. It is found that a point mass located at one side of the circle can generate almost the same strength of gravitational force at the…
We classify the simple linear compactifications of SO(2r+1), namely those compactifications with a unique closed orbit which are obtained by taking the closure of the SO(2r+1)xSO(2r+1)-orbit of the identity in a projective space P(End(V)),…
We provide a natural smooth projective compactification of the space of algebraic maps from the projective line to the projective space of dimension n by adding a divisor with simple normal crossings.
The cascade relaxation of a polarized vacuum in the expanding Universe is a chain of evolutionary epochs of decreasing its density with the exit of dominant fields (each in its own time) from the initial zero states to nonzero values, from…
We propose a novel technique, termed compact shape trees, for computing correspondences of single-boundary 2-D shapes in O(n2) time. Together with zero or more features defined at each of n sample points on the shape's boundary, the compact…
In the current review, we provide a summary of the recent progress made in the cosmological aspect of extra-dimensional Lovelock gravity. Our review covers a wide variety of particular model/matter source combinations:…
The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…
In this paper, we analyze the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor associated with a charged and massive scalar quantum field in a generalized $(D+1)$-dimensional anti-de Sitter space in the…
We give detailed proofs of several new no-go theorems for constructing flat four-dimensional accelerating universes from warped dimensional reduction. These new theorems improve upon previous ones by weakening the energy conditions, by…
To an $\mathbb{R}$-tree in the boundary of Outer space, we associate two simplices: the simplex of projective length measures, and the simplex of projective dual currents. For both kinds of simplices, we estimate the dimension of maximal…
One of the drawbacks of conventional grand unification scenarios has been that the unification scale is too high to permit direct exploration. In this paper, we show that the unification scale can be significantly lowered (perhaps even to…