Related papers: Cosmic Divergence, Weak Cosmic Convergence, and Fi…
We discuss some basic properties of polar convergence in metric spaces. Polar convergence is closely connected with the notion of Delta-convergence of T.C. Lim known for several years. Possible existence of a topology which induces polar…
The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…
In this paper, we discuss characterizations of common fixed points of commutative semigroups of nonexpansive mappings. We next prove convergence theorems to a common fixed point. We finally discuss nonexpansive retractions onto the set of…
Because of Minty's classical correspondence between firmly nonexpansive mappings and maximally monotone operators, the notion of a firmly nonexpansive mapping has proven to be of basic importance in fixed point theory, monotone operator…
Cosmological singularity theorems such as that of Hawking and Penrose assume local curvature conditions as well as global ones like the existence of a compact (achronal) slice. Here, we prove a new singularity theorem for chronological…
We introduce a new class of asymptotic contractions that employs two quasi-metrics defined directly in terms of the underlying mapping. The contraction condition compares these two quantities via a sequence of bounding functions that…
We discuss how entropy bounds, which are not respected in the standard cosmology, constrain the parameters of a previously suggested cosmology with a finite total mass. In that alternative cosmology the matter density was postulated to be a…
The observed late-time acceleration of the cosmic expansion constitutes a fundamental problem in modern theoretical physics and cosmology. In an attempt to weight the validity of a large number of dark energy models, I use the recent…
This note discusses some aspects of the asymptotic behaviour of nonexpansive maps. Using metric functionals, we make a connection to the invariant subspace problem and prove a new result for nonexpansive maps of $\ell^{1}$. We also point…
Advantages of inhomogeneous cosmological models that are exact solutions of Einstein's equations over linearised perturbations of homogeneous models are presented. Examples of effects that can be described in the inhomogeneous ones are…
We propose an approach to explaining why naive large quantum fluctuations are not the right estimate for the cosmological constant. We argue that the universe is in a superposition of many vacua, in such a way that the resulting…
The product of two empirical constants, the dimensionless fine structure constant and the von Klitzing constant (an electrical resistance), turns out to be an exact dimensionless number. Then the accuracy and cosmological time variation (if…
We define the infinite dimensional simplex to be the closure of the convex hull of the standard basis vectors in R^infinity, and prove that this space has the 'fixed point property': any continuous function from the space into itself has a…
In a recent work, it has been proposed that the recent cosmic passage to a cosmic acceleration era is the result of the existence of small anti-gravity sources in each galaxy and clusters of galaxies. In particular, a swiss-cheese cosmology…
We study quantum gravity in more than four dimensions by means of an exact functional flow. A non-trivial ultraviolet fixed point is found in the Einstein-Hilbert theory. It is shown that our results for the fixed point and universal…
The current expansion of the Universe has been observed to be accelerating, and the widely accepted spatially-flat concordance model of general relativistic cosmology attributes this phenomenon to a constant dark energy, a cosmological…
In this thesis, we scrutinize the literature to trace the evolution of the concepts surrounding the weak cosmic censorship conjecture and the attempts to prove or disprove it. We discuss its development over the years, its conceptual…
Mach's "fixed stars" are actually not fixed at all. The distant clusters of galaxies are not only receding from each observer but they are also accelerating since the rate of cosmological expansion is not constant. If the distant cosmic…
Let C be a nonempty, bounded, closed, and convex subset of a Banach space X and $T : C \rightarrow C$ be a monotone asymptotic nonexpansive mapping. In this paper, we investigate the existence of fixed points of T. In particular, we…
The discovery of accelerated cosmic expansion implies that, in addition to the attractive gravity of matter, there exists in our universe some other form of energy (dark energy or cosmological constant) producing a repulsive force. The…