Related papers: Lower Bound For Dilatations

We give explicit isoperimetric upper bounds for all Steklov eigenvalues of a compact orientable surface with boundary, in terms of the genus, the length of the boundary, and the number of boundary components. Our estimates generalize a…

This is an addendum to the paper of Braun and Fl{\o}ystad ([BF]) on the bound for the degree of a smooth surface in $\pfour$ not of general type. Using their construction and the regularity of curves in $\pthree$, one may lower the bound a…

Covering numbers are a powerful tool used in the development of approximation algorithms, randomized dimension reduction methods, smoothed complexity analysis, and others. In this paper we prove upper bounds on the covering number of…

Given a graph G with vertex set V, a subset S of V is a dominating set if every vertex in V is either in S or adjacent to some vertex in S. The size of a smallest dominating set is called the domination number of G. We study a variant of…

Pseudoline arrangements are fundamental objects in discrete and computational geometry, and different works have tackled the problem of improving the known bounds on the number of simple arrangements of $n$ pseudolines over the past…

In this paper, we propose new lower and upper bounds on the linear extension complexity of regular $n$-gons. Our bounds are based on the equivalence between the computation of (i) an extended formulation of size $r$ of a polytope $P$, and…

We give a new asymptotic upper bound on the size of a code in the Grassmannian space. The bound is better than the upper bounds known previously in the entire range of distances except very large values.

The purpose of this paper is to establish an upper bound on the distance between two pants decompositions in the pants complex for a closed surface of genus g >= 2. This is done by use of graph theory. First distance is found in the pants…

In this article, we study the topological complexity of manifolds with a lower scalar curvature bound. We introduce a small scale index theorem to establish an upper bound for Gromov's simplicial norm of the Poincar\'e dual of the A-hat…

We prove a strong general-purpose bound for the diameter of a finite group depending only on the diameters of its composition factors and the maximal exponent of a normal abelian section. There are a number of notable applications: (1) if…

We prove Poisson approximation results for the bottom part of the length spectrum of a random closed hyperbolic surface of large genus. Here, a random hyperbolic surface is a surface picked at random using the Weil-Petersson volume form on…

Let $G$ be a connected semisimple real algebraic group. We prove that limit cones vary continuously under deformations of Anosov subgroups of $G$ under a certain convexity assumption, which turns out to be necessary. We apply this result to…

We give an improved lower bound for the $L_2$-discrepancy of finite point sets in the unit square.

We prove that, in the $l$-ball of the Cayley graph of the braid group with $n \geqslant 3$ strands, the proportion of rigid pseudo-Anosov braids is bounded below independently of $l$ by a positive value.

This article follows and completes [arXiv:2511.14222], where we study the problem of bounded deviations for homeomorphisms of closed surfaces of genus $\ge 2$. This second part deals with bounded deviations relative to geodesic minimal…

Under reasonable working assumptions including the polynomial boundedness, one proves the well-known Cerulus-Martin lower bound on how fast an elastic scattering amplitude can decrease in the hard-scattering regime. In this paper we…

For general one-matrix models in the large $N$ limit, we introduce the cap amplitude $\psi(b)$ as the expansion coefficient of the 1-form $ydx$ on the spectral curve. We find that the dilaton equation for the discrete volume $N_{g,n}$ of…

We show that perturbing the definition of sl(n) Khovanov-Rozansky link homology gives a lower bound on the slice genus of a knot. As a corollary this yields another proof of Milnor's conjecture on the slice genus of torus knots.

In this paper we give a short, new proof of a natural generalization of Gerzon's bound. This bound improves the Delsarte, Goethals and Seidel's upper bound in a special case. Our proof is a simple application of the linear algebra bound…

In this paper, we study Alexandrov-embedded r-noids with genus 1 and horizontal ends. Such minimal surfaces are of two types and we build several examples of the first one. We prove that if a polygon bounds an immersed polygonal disk, it is…