Related papers: Some spherical coverings on S2 and their algebraic…
This article provides an overview of the techniques related to classification of spherical and more general objects within triangulated categories, and its relationship with algebraic geometry, representation theory and symplectic geometry.…
We survey the classification of the Riemannian metrics on spheres with respect to which all equators are minimal hypersurfaces, and discuss problems related to these geometries.
We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In…
This paper investigates the behaviour of the kissing number $\kappa(n, r)$ of congruent radius $r > 0$ spheres in $\mathbb{S}^n$, for $n\geq 2$. Such a quantity depends on the radius $r$, and we plot the approximate graph of $\kappa(n, r)$…
Algebraic surfaces in the complex projective space with a high number of A-type singularities have been presented in a recent paper. We extend the construction in order to obtain lower bounds for the maximal number of A singularities for…
This paper has two agendas. Firstly, we exhibit new results for coverage processes. Let $p(n,m,\alpha)$ be the probability that $n$ spherical caps of angular radius $\alpha$ in $S^m$ do not cover the whole sphere $S^m$. We give an exact…
We present filling as a new type of spatial subdivision problem that is related to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most…
Denote by $S^2$ the two-dimensional sphere. A spherical convex body on $S^2$ which does not properly contain a spherical convex body of the same spherical thickness is called a reduced body. We give three characterizations of reducedness of…
In this talk we show that any spherically symmetric spacetime admits locally a maximal spacelike slicing. The above condition is reduced to solve a decoupled system of first order quasi-linear partial differential equations. The solution…
This paper develops a systematic and geometric theory of optimal quantization on the unit sphere $\mathbb S^2$, focusing on finite uniform probability distributions supported on the spherical surface - rather than on lower-dimensional…
In this article, we consider `$N$'spherical caps of area $4\pi p$ were uniformly distributed over the surface of a unit sphere. We are giving the strong threshold function for the size of random caps to cover the surface of a unit sphere.…
We obtain uncountably many periodic solutions to the singular Yamabe problem on a round sphere, that blow up along a great circle. These are (complete) constant scalar curvature metrics on the complement of $S^1$ inside $S^m$, $m\geq 5$,…
In this article we investigate the $N$-point min-max and the max-min polarization problems on the sphere for a large class of potentials in $\mathbb{R}^n$. We derive universal lower and upper bounds on the polarization of spherical designs…
This work is a survey on completely regular codes. Known properties, relations with other combinatorial structures and constructions are stated. The existence problem is also discussed and known results for some particular cases are…
Spherical spin glasses are canonical models for smooth random functions in high dimensions. In this review, we survey several interrelated lines of research on their geometric structure. We begin with results concerning critical points and…
We develop a systematic framework for constructing spherical harmonics on the two-dimensional unit sphere as superpositions of Gaussian beams whose poles form well-separated point configurations. The distributional and analytic properties…
Lebesgue's universal covering problem is re-examined using computational methods. This leads to conjectures about the nature of the solution which if correct could provide a blueprint for a complete solution. Empirical lower bounds for the…
Methodology is provided towards the solution of the minimum enclosing ball problem. This problem concerns the determination of the unique spherical surface of smallest radius enclosing a given bounded set in the d-dimensional Euclidean…
For a finite planar graph, it associates with some metric spaces, called (regular) spherical polyhedral surfaces, by replacing faces with regular spherical polygons in the unit sphere and gluing them edge-to-edge. We consider the class of…
We derive optimal filters on the sphere in the context of detecting compact objects embedded in a stochastic background process. The matched filter and the scale adaptive filter are derived on the sphere in the most general setting,…