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Related papers: Bounds on entries in Bianchi group generators

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In this paper we provide explicit upper and lower bounds on certain $L^2$ $n$-widths, i.e., best constants in $L^2$ approximation. We further describe a numerical method to compute these $n$-widths approximately, and prove that this method…

Numerical Analysis · Mathematics 2020-09-28 Andrea Bressan , Michael S. Floater , Espen Sande

We give upper bounds on the size of the gap between a non-zero constant term and the next non-zero Fourier coefficient of an entire level two modular form. We give upper bounds for the minimum positive integer represented by a level two…

Number Theory · Mathematics 2015-06-26 Barry Brent

We prove the existence of positive lower bounds on the Cheeger constants of manifolds of the form $X/\Gamma$ where $X$ is a contractible Riemannian manifold and $\Gamma<\Isom(X)$ is a discrete subgroup, typically with infinite co-volume.…

Geometric Topology · Mathematics 2015-11-03 Lewis Bowen

This paper provides the currently best known upper bound on the density of a packing in three-dimensional Euclidean space of two types of spheres whose size ratio is the largest one that allows the insertion of a small sphere in each…

Metric Geometry · Mathematics 2025-05-21 Thomas Fernique , Daria Pchelina

For a conformally compact manifold that is hyperbolic near infinity and of dimension $n+1$, we complete the proof of the optimal $O(r^{n+1})$ upper bound on the resonance counting function, correcting a mistake in the existing literature.…

Spectral Theory · Mathematics 2011-11-10 David Borthwick

We prove that the lacunary spherical maximal operator, defined on the $n$-dimensional real hyperbolic space, is bounded on $L^p(\mathbb{H}^n)$ for all $n\ge2$ and $1<p\le\infty$. In particular, the lacunary set is significantly larger than…

Classical Analysis and ODEs · Mathematics 2025-03-03 Yunxiang Wang , Hong-Wei Zhang

On a complete noncompact K\"{a}hler manifold we prove that the bottom of the spectrum for the Laplacian is bounded from above by $m^2$ if the Ricci curvature is bounded from below by $-2(m+1)$. Then we show that if this upper bound is…

Differential Geometry · Mathematics 2007-05-23 Ovidiu Munteanu

We give a new lower bound for the first gap $\lambda_2 - \lambda_1$ of the Dirichlet eigenvalues of the Schr{\"o}dinger operator on a bounded convex domain $\Omega$ in R$^n$ or S$^n$ and greatly sharpens the previous estimates. The new…

Differential Geometry · Mathematics 2007-05-23 Jun Ling

Given two pants decompositions of a compact orientable surface $S$, we give an upper bound for their distance in the pants graph that depends logarithmically on their intersection number and polynomially on the Euler characteristic of $S$.…

Geometric Topology · Mathematics 2025-11-06 Marc Lackenby , Mehdi Yazdi

We show that the cyclic lamplighter group $C_2 \bwr C_n$ embeds into Hilbert space with distortion ${\rm O}(\sqrt{\log n})$. This matches the lower bound proved by Lee, Naor and Peres in \cite{LeeNaoPer}, answering a question posed in that…

Metric Geometry · Mathematics 2007-06-13 Tim Austin , Assaf Naor , Alain Valette

Let $\Gamma\subset \textrm{PSL}_2({\mathbb R})$ be a Fuchsian group of the first kind having a fundamental domain with a finite hyperbolic area, and let $\widetilde\Gamma$ be its cover in $\textrm{SL}_2({\mathbb R})$. Consider the space of…

Number Theory · Mathematics 2020-02-24 Yasemin Kara , Moni Kumari , Jolanta Marzec , Kathrin Maurischat , Andreea Mocanu , Lejla Smajlović

The number of lattice points in $d$-dimensional hyperbolic or elliptic shells $\{m : a<Q[m]<b\}$, which are restricted to rescaled and growing domains $r\;\Omega$, is approximated by the volume. An effective error bound of order…

Number Theory · Mathematics 2021-11-16 Paul Buterus , Friedrich Götze , Thomas Hille , Gregory Margulis

We give a method for computing upper and lower bounds for the volume of a non-obtuse hyperbolic polyhedron in terms of the combinatorics of the 1-skeleton. We introduce an algorithm that detects the geometric decomposition of good…

Geometric Topology · Mathematics 2012-11-22 Christopher K. Atkinson

A spherical $L$-code, where $L \subseteq [-1,\infty)$, consists of unit vectors in $\mathbb{R}^d$ whose pairwise inner products are contained in $L$. Determining the maximum cardinality $N_L(d)$ of an $L$-code in $\mathbb{R}^d$ is a…

Combinatorics · Mathematics 2023-12-01 Saba Lepsveridze , Aleksandre Saatashvili , Yufei Zhao

In this paper, we use a weighted isoperimetric inequality to give a lower bound on the first Dirichlet eigenvalue of the Laplacian on a bounded domain inside a Euclidean cone. Our bound is sharp, in that only sectors realize it. This result…

Analysis of PDEs · Mathematics 2016-02-02 Jesse Ratzkin

Inspired by the boolean discrepancy problem, we study the following optimization problem which we term \textsc{Spherical Discrepancy}: given $m$ unit vectors $v_1, \dots, v_m$, find another unit vector $x$ that minimizes $\max_i \langle x,…

Computational Complexity · Computer Science 2019-11-19 Chris Jones , Matt McPartlon

We prove that the maximum eigenvalue of the (both signed and unsigned) Laplacian of level $k$ Kikuchi graph of any graph $G$ with $m$ edges is at most $m+k$. This confirms four recent conjectures of Apte, Parekh, and Sud. As applications,…

Quantum Physics · Physics 2026-05-15 Ainesh Bakshi , Arpon Basu , Pravesh Kothari , Anqi Li

Let $\Lambda$ be an artin algebra. We give an upper bound for the dimension of the bounded derived category of the category $\mod \Lambda$ of finitely generated right $\Lambda$-modules in terms of the projective and injective dimensions of…

Rings and Algebras · Mathematics 2020-04-30 Junling Zheng , Zhaoyong Huang

Let $G$ be a group that is relatively hyperbolic with respect to a collection of subgroups $\{H_{\lambda}\}_{\lambda\in \Lambda}$. Suppose that $G$ is given by a finite relative presentation $\mathcal{P}$ with respect to this collection. We…

Group Theory · Mathematics 2025-01-09 Oleg Bogopolski

Arrangements of lines and pseudolines are fundamental objects in discrete and computational geometry. They also appear in other areas of computer science, such as the study of sorting networks. Let $B_n$ be the number of nonisomorphic…

Combinatorics · Mathematics 2018-12-10 Adrian Dumitrescu , Ritankar Mandal