Related papers: Planar Projections and Second Intrinsic Volume
An important idea underlying a plausible dynamical theory of circulation in three-dimensional turbulence is the so-called Area Rule, according to which the probability density function (PDF) of the circulation around closed loops depends…
The observational "black holes" are quite different objects from the theoretical black holes.
We characterize symmetric spaces of non-positive curvature by the equality case of general inequalities between geometric quantities
In this paper, we study the curvature properties of random complex plane curves. We bound from below the probability that a uniform proportion of the area of a random complex degree $d$ plane curve has a curvature smaller than $-d/8$. Our…
General relativistic imprints on the galaxy bispectrum arise from observational (or projection) effects. The lightcone projection effects include local contributions from Doppler and gravitational potential terms, as well as lensing and…
The properties of the hollow beam produced by a conical lens are studied in detail. In particular, the impact of a rounded vertex is examined. It is shown that it could lead to drastic changes in the transverse distribution of the hollow…
A dynamical symmetry for spherical collapse has been studied using a linear transformation of the initial data set (mass and kinetic energy function) and the area radius. With proper choice of the initial area radius, the evolution as well…
Positive geometries encode the physics of scattering amplitudes in flat space-time and the wavefunction of the universe in cosmology for a large class of models. Their unique canonical forms, providing such quantum mechanical observables,…
The properties of precessing, coalescing binary black holes are presently inferred through comparison with two approximate models of compact binary coalescence. In this work we show these two models often disagree substantially when…
A shadow of a geometric object $A$ in a given direction $v$ is the orthogonal projection of $A$ on the hyperplane orthogonal to $v$. We show that any topological embedding of a circle into Euclidean $d$-space can have at most two shadows…
Subdominant contributions to the entanglement entropy of quantum fields include logarithmic corrections to the area law characterized by universal coefficients that are independent of the ultraviolet regulator and capture detailed…
Within classical optics, one may add microscopic "roughness" to a macroscopically flat mirror so that parallel rays of a given angle are reflected at different outgoing angles. Taking the limit (as the roughness becomes increasingly…
We consider the reflection from a random medium of light with short coherence length. We found that the second order correlation function of light can have a peak in a direction where the reflection angle is equal to angle of incidence.…
Intrinsic volumes, which generalize both Euler characteristic and Lebesgue volume, are important properties of $d$-dimensional sets. A random cubical complex is a union of unit cubes, each with vertices on a regular cubic lattice,…
Existence of nicely bounded sections of two symmetric convex bodies K and L implies that the intersection of random rotations of K and L is nicely bounded. For L = subspace, this main result immediately yields the unexpected phenomenon: "If…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multiply rather than simply connected. We review the main mathematical properties of multiply connected spaces, and the different…
It is argued that the standard quantum mechanical description of the Bell correlations between entangled subsystems is in conflict with relativistic space-time symmetry. Proposals to abandon relativistic symmetry, in the sense of explicitly…
Upcoming surveys of cosmic structures will probe scales close to the cosmological horizon, which opens up new opportunities for testing the cosmological concordance model to high accuracy. In particular, constraints on the squeezed…
We consider the number of configurations of a surface in two dimensions that has a prescribed length and encloses a prescribed perimeter with respect to a baseline. An approximate analytical treatment in a semi--continuum compares…
We show that it is possible to decide whether a given planar diagram correctly depicts the spatial figure consisting of a planar quadrangle together with its shadow in another plane.