Related papers: Sphere paths in outer space
We determine the local geometric structure of two-dimensional metric spaces with curvature bounded above as the union of finitely many properly embedded/branched immersed Lipschitz disks. As a result, we obtain a graph structure of the…
The standard arithmetic measures of center, the mean and median, have natural topological counterparts which have been widely used in continuum theory. In the context of metric spaces it is natural to consider the Lipschitz continuous…
We consider the direction set determined by various subsets $E$ of Euclidean space and show that there is a trichotomy: Either (i) The subset is the graph of a Lipschitz function and the direction set is not dense in the sphere, (ii) The…
We survey many of the important properties of spherically symmetric spacetimes as follows. We present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an…
The aim of this paper is to associate a measure for certain sets of paths in the Euclidean plane $\mathbb{R}^2$ with fixed starting and ending points. Then, working on parameterized surfaces with a specific Riemannian metric, we define and…
The light curve of an exoplanetary transit can be used to estimate the planetary radius and other parameters of interest. Because accurate parameter estimation is a non-analytic and computationally intensive problem, it is often useful to…
We study the metric structure of walks on graphs, understood as Lipschitz sequences. To this end, a weighted metric is introduced to handle sequences, enabling the definition of distances between walks based on stepwise vertex distances and…
This chapter reviews some past and recent developments in shape comparison and analysis of curves based on the computation of intrinsic Riemannian metrics on the space of curves modulo shape-preserving transformations. We summarize the…
Infinite graphs are finitary in the sense that their points are connected via finite paths. So what would an infinitary generalization of finite graphs look like? Usually this question is answered with the aid of topology, e.g. in the case…
Optical interferometry provides us with a unique opportunity to improve our understanding of stellar structure and evolution. Through direct observation of rotationally distorted photospheres at sub-milliarcsecond scales, we are now able to…
We study the spatial distribution of point sets on the sphere obtained from the representation of a large integer as a sum of three integer squares. We examine several statistics of these point sets, such as the electrostatic potential,…
The presence of silicate material in known rings in the Solar System raises the possibility of ring systems existing even within the snow line -- where most transiting exoplanets are found. Previous studies have shown that the detection of…
Context. Thanks to recent large scale surveys in the near infrared such as 2MASS, the galactic plane that most suffers from extinction is revealed and its overall structure can be studied. Aims. This work aims at constraining the structure…
In this paper we study the continuity of the Berezin transform on modified Bergman spaces and we establish a Lipschitz estimate in terms of the Bergman-Poincar\'e metric.
A recent generalization of the Erd\H{o}s Unit Distance Problem, proposed by Palsson, Senger and Sheffer, asks for the maximum number of unit distance paths with a given number of vertices in the plane and in $3$-space. Studying a variant of…
There is a growing interest in developing covariance functions for processes on the surface of a sphere due to wide availability of data on the globe. Utilizing the one-to-one mapping between the Euclidean distance and the great circle…
Motion of a point mass in gravitational fields of the Sun and of the galactic disk is studied. Fundamental features of the motion are found by investigating the time-averaged differential equations for orbital evolution. Several types of…
Any space-filling packing of spheres can be cut by a plane to obtain a space-filling packing of disks. Here, we deal with space-filling packings generated using inversive geometry leading to exactly self-similar fractal packings. First, we…
The large-scale structure of the Universe is well approximated by the Friedmann equations, parametrized by several energy densities which can be observationally inferred. A natural question to ask is: How different would the Universe be if…
In this paper we study the boundedness of extension operators associated with spheres in vector spaces over finite fields.In even dimensions, we estimate the number of incidences between spheres and points in the translated set from a…