Related papers: Small cones of oriented semi-metrics

Thanks to recent advances in parametric geometry of numbers, we know that the spectrum of any set of $m$ exponents of Diophantine approximation to points in $\mathbb{R}^n$ (in a general abstract setting) is a compact connected subset of…

We classify the Q-polynomial association schemes with $m_{1} = 4$ which are partially metric with respect to the nearest neighbourhood relation. An association scheme is partially metric with respect to a relation $R_1$ if the scheme graph…

Several recent papers have explored families of rational polyhedra whose integer points are in bijection with certain families of numerical semigroups. One such family, first introduced by Kunz, has integer points in bijection with…

We prove that each lower-dimensional face of a quasi-arithmetic Coxeter polytope, which happens to be itself a Coxeter polytope, is also quasi-arithmetic. We also provide a sufficient condition for a codimension $1$ face to be actually…

A convex cone is said to be projectionally exposed (p-exposed) if every face arises as a projection of the original cone. It is known that, in dimension at most four, the intersection of two p-exposed cones is again p-exposed. In this paper…

This article is concerned with the approximation of unbounded convex sets by polyhedra. While there is an abundance of literature investigating this task for compact sets, results on the unbounded case are scarce. We first point out the…

This paper presents formulae for calculation the solid angle of intersecting spherical caps, conical surfaces and polyhedral cones.

In this work we take a deep dive into the cone of copositive $3 \times 3$ matrices. In doing so we visualize the cone, make geometric observations about it, and prove them. We then use these observations to parametrize the set. In the…

We revisit classical Virtual Element approximations on polygonal and polyhedral decompositions. We also recall the treatment proposed for dealing with decompositions into polygons with curved edges. In the second part of the paper we…

The aim of this paper is to study generalized recurrent, generalized Ricci-recurrent, weakly symmetric and weakly Ricci-symmetric Kenmotsu manifolds with respect to the semi-symmetric non-metric connection.

The diameter of the graph of a $d$-dimensional polyhedron with $n$ facets is at most $n^{\log d+2}$

We study two notions. One is that of spindle convexity. A set of circumradius not greater than one is spindle convex if, for any pair of its points, it contains every short circular arc of radius at least one, connecting them. The other…

We study balls of homogeneous cubics on $\mathbb R^n$, $n = 2,3$, which are bounded by unity on the unit sphere. For $n = 2$ we completely describe the facial structure of this norm ball, while for $n = 3$ we classify all extremal points…

It is introduced a differentiable manifold with almost contact 3-structure which consists of an almost contact metric structure and two almost contact B-metric structures. The product of this manifold and a real line is an almost…

In this article, we solve the relative isoperimetric problem in $[0,1]^3$ for orthogonal polyhedra. Up to isometries of the cube or sets of measure $0$, the minimizers are of the form $[0,\epsilon]^3$, $[0,\epsilon]^2 \times [0,1]$, or…

We study the problem of approximating the cone of positive semidefinite (PSD) matrices with a cone that can be described by smaller-sized PSD constraints. Specifically, we ask the question: "how closely can we approximate the set of…

We introduce the {\em pair-cut cone $PCUT_n$} of metrics on sets with $n\ge 3$ elements, that correspond to linear combinations with non-negative coefficients of the cut-metrics resulting from cuts that are pairs. Given a metric, we fully…

We study generalizations of classical metric embedding results to the case of quasimetric spaces; that is, spaces that do not necessarily satisfy symmetry. Quasimetric spaces arise naturally from the shortest-path distances on directed…

Different commutative semigroups may have a common saturation. We consider distinguishing semigroups with a common saturation based on their ``sparsity''. We propose to qualitatively describe sparsity of a semigroup by considering which…

We construct new examples of contact manifolds in arbitrarily large dimensions. These manifolds which we call quasi moment-angle manifolds, are closely related to the classical moment-angle manifolds.