Related papers: Asymmetry of Outer Space
Astronomical observations showed that there may exist a bulk flow with peculiar velocities in the universe, which contradicts with the (\Lambda)CDM model. The bulk flow reveals that the observational universe is anisotropic at large scales.…
For a finitely generated group $G$, we introduce an asymmetric pseudometric on projectivized deformation spaces of $G$-trees, using stretching factors of $G$-equivariant Lipschitz maps, that generalizes the Lipschitz metric on Outer space…
In this paper, we answer some natural questions on symmetrisation and more general combinations of Finsler metrics, with a view towards applications to Funk and Hilbert geometries and to metrics on Teichm{\"u}ller spaces. For a general…
We obtain an optimal deviation from the mean upper bound \begin{equation} D(x)\=\sup_{f\in \F}\mu\{f-\E_{\mu} f\geq x\},\qquad\ \text{for}\ x\in\R\label{abstr} \end{equation} where $\F$ is the class of the integrable, Lipschitz functions on…
In the first part Busemann concavity as non-negative curvature is introduced and a bi-Lipschitz splitting theorem is shown. Furthermore, if the Hausdorff measure of a Busemann concave space is non-trivial then the space is doubling and…
Density of Lipschitz functions in Newtonian spaces based on quasi-Banach function lattices is discussed. Newtonian spaces are first-order Sobolev-type spaces on abstract metric measure spaces defined via (weak) upper gradients. Our main…
Along with the construction of non-Lorentz-invariant effective field theories, recent studies which are based on geometric models of Finsler space-time become more and more popular. In this respect, the Finslerian approach to the problem of…
We quantitatively relate the Patterson-Sullivant currents and generic stretching factors for free group automorphisms to the asymmetric Lipschitz metric on Outer space and to Guirardel's intersection number.
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a "box." This breaks symmetries, though the breaking is small when the box is large. One should thus be able to…
We prove a rigidity theorem that shows that, under many circumstances, quasi-isometric embeddings of equal rank, higher rank symmetric spaces are close to isometric embeddings. We also produce some surprising examples of quasi-isometric…
We discuss the spatial limit of the quasi-local mass for certain ellipsoids in an asymptotically flat static spherically symmetric spacetime. These ellipsoids are not nearly round but they are of interest as an admissible parametrized…
Finsler geometry is just riemannian geometry without the quadratic restriction[1]. In this paper, we study the motion of massive(non-zero rest mass) and massless particles for schwarzschild metric in finsler spacetime in the case of two…
For a given metric measure space $(X,d,\mu)$ we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS)…
We present a phenomenological model for the nature in the Finsler and Randers space-time geometries. We show that the parity-odd light speed anisotropy perpendicular to the gravitational equipotential surfaces encodes the deviation from the…
If a non-reversible Finsler norm is the sum of a reversible Finsler norm and a closed 1-form, then one can uniquely recover the 1-form up to potential fields from the boundary distance data. We also show a boundary rigidity result for…
In this paper, we introduce an asymmetric metric on the space of marked Euclidean triangles, and we prove several properties of this metric, including two equivalent definitions of this metric, one of them comparing ratios of functions of…
We show that the norm of the commutator defines "almost a metric" on the quotient space of commuting matrices, in the sense that it is a semi-metric satisfying the triangle inequality asymptotically for large matrices drawn from a "good"…
We consider extensions of quasiconformal maps and the uniformization theorem to the setting of metric spaces $X$ homeomorphic to $\mathbb R^2$. Given a measure $\mu$ on such a space, we introduce $\mu$-quasiconformal maps $f:X \to \mathbb…
We relate ergodic-theoretic properties of a very small tree or lamination to the behavior of folding and unfolding paths in Outer space that approximate it, and we obtain a criterion for unique ergodicity in both cases. Our main result is…
According to the socalled "quasi-metric" framework developed elsewhere, the cosmic expansion applies directly to gravitationally bound systems. This prediction has a number of observable consequences, none of which are in conflict with…