Related papers: The hull metric on Coxeter groups

A spectrahedron is a set defined by a linear matrix inequality. A projection of a spectrahedron is often called a semidefinitely representable set. We show that the convex hull of a finite union of such projections is again a projection of…

In this article, we focus on establishing a new variant of Hermite-Hadamard type inequalities for operator convex maps using an appropriate probability measure. To underline the usefulness of these inequalities, we investigate some…

We examine the metrics that arise when a finite set of points is embedded in the real line, in such a way that the distance between each pair of points is at least 1. These metrics are closely related to some other known metrics in the…

We prove that the hitting measure is singular with respect to Lebesgue measure for any random walk on a cocompact Fuchsian group generated by translations joining opposite sides of a symmetric hyperbolic polygon. Moreover, the Hausdorff…

In the present work, we consider Zuckerberg's method for geometric convex-hull proofs introduced in [Geometric proofs for convex hull defining formulations, Operations Research Letters 44(5), 625-629 (2016)]. It has only been scarcely…

We introduce a notion of convex hull and polytope into adele space. This allows to consider adelic triangulations which, in particular, lead to an adelic blichfeldt-type inequality, complementing former results.

We study properties of convex hulls of (co)adjoint orbits of compact groups, with applications to invariant theory and tensor product decompositions. The notion of partial convex hulls is introduced and applied to define two numerical…

The rank of a hierarchically hyperbolic space is the maximal number of unbounded factors in a standard product region. For hierarchically hyperbolic groups, this coincides with the maximal dimension of a quasiflat. Examples for which the…

Let $C$ be a proper convex cone generated by a compact set which supports a measure $\mu$. A construction due to A.Barvinok, E.Veomett and J.B. Lasserre produces, using $\mu$, a sequence $(P_k)_{k\in \mathbb{N}}$ of nested spectrahedral…

We derive a closed form description of the convex hull of mixed-integer bilinear covering set with bounds on the integer variables. This convex hull description is determined by considering some orthogonal disjunctive sets defined in a…

A classical approach for obtaining valid inequalities for a set involves weighted aggregations of the inequalities that describe such set. When the set is described by linear inequalities, thanks to the Farkas lemma, we know that every…

In this article we study Sobolev metrics of order one on diffeomorphism groups on the real line. We prove that the space $\operatorname{Diff}_{1}(\mathbb R)$ equipped with the homogenous Sobolev metric of order one is a flat space in the…

We study asymptotic estimates of the dimension of cohomology on possibly non-compact complex manifolds for line bundles endowed with Hermitian metrics with algebraic singularities. We give a unified approach to establishing singular…

The H-unistochastic matrices are a special class of symmetric bistochastic matrices obtained by taking the square of the absolute value of each entry of a Hermitian unitary matrix. We examine the geometric relationship of the convex hull of…

A conjecture proposed by Gaetz and Gao asserts that the Cayley graph of any Coxeter group satisfies the strong hull property. In this paper, we prove this conjecture for all affine irreducible Coxeter groups of rank 3. Our approach exploits…

A well-known family of determinantal inequalities for mixed volumes of convex bodies were derived by Shephard from the Alexandrov-Fenchel inequality. The classic monograph Geometric Inequalities by Burago and Zalgaller states a conjecture…

In this paper, is introduced a new proposal of resolvent for equilibrium problems in terms of the Busemann's function. A great advantage of this new proposal is that, in addition to be a natural extension of the proposal in the linear…

We prove new concentration estimates for random variables that are functionals of a Poisson measure defined on a general measure space. Our results are specifically adapted to geometric applications, and are based on a pervasive use of a…

The open intervals in the Bruhat order on twisted involutions in a Coxeter group are shown to be PL spheres. This implies results conjectured by F. Incitti and sharpens the known fact that these posets are Gorenstein* over Z_2. We also…

This is both an expository and research paper where we advocate a systematic study of continuous analogues of finite partially ordered sets, convex polytopes, oriented matroids, arrangements of subspaces, finite simplicial complexes, and…