Related papers: On Cheeger constants of hyperbolic surfaces

Brooks and Makover developed a combinatorial model of random hyperbolic surfaces by gluing certain hyperbolic ideal triangles. In this paper we show that for any $\epsilon>0$, as the number of ideal triangles goes to infinity, a generic…

Let $d \geq 2$. The Cheeger constant of a graph is the minimum surface-to-volume ratio of all subsets of the vertex set with relative volume at most 1/2. There are several ways to define surface and volume here: the simplest method is to…

We give a brief literature review of the isoperimetric problem and discuss its relationship with the Cheeger constant of Riemannian $n$-manifolds. For some non-compact, finite area 2-manifolds, we prove the existence and regularity of…

We compute the Cheeger constants of a collection of hyperbolic surfaces corresponding to maximal non-compact arithmetic Fuchsian groups, and to subgroups which are the rotation subgroup of maximal reflection groups. The Cheeger constants…

We show that the Cheeger constant of compact surfaces is bounded by a function of the area. We apply this to isoperimetric profiles of bounded genus non-compact surfaces, to show that if their isoperimetric profile grows faster than $\sqrt…

The Cheeger constant of an open set of the Euclidean space is defined by minimizing the ratio "perimeter over volume", among all its smooth compactly contained subsets. We consider a natural variant of this problem, where the volume of…

We are interested in finding sharp bounds for the Cheeger constant $h$ via different geometrical quantities, namely the area $|\cdot|$, the perimeter $P$, the inradius $r$, the circumradius $R$, the minimal width $\omega$ and the diameter…

Let $\mathcal{M}_{g,n(g)}$ be the moduli space of hyperbolic surfaces of genus $g$ with $n(g)$ punctures endowed with the Weil-Petersson metric. In this paper we study the asymptotic behavior of the Cheeger constants and spectral gaps of…

In this paper we prove a new extremal property of the Reuleaux triangle: it maximizes the Cheeger constant among all bodies of (same) constant width. The proof relies on a fine analysis of the optimality conditions satisfied by an optimal…

We prove Cheeger inequalities for p-Laplacians on finite and infinite weighted graphs. Unlike in previous works, we do not impose boundedness of the vertex degree, nor do we restrict ourselves to the normalized Laplacian and, more…

In this paper we study the asymptotic behavior of Weil-Petersson volumes of moduli spaces of hyperbolic surfaces of genus $g$ as $g \rightarrow \infty.$ We apply these asymptotic estimates to study the geometric properties of random…

The Cheeger constant of a graph is the smallest possible ratio between the size of a subgraph and the size of its boundary. It is well known that this constant must be at least $\frac{\lambda_1}{2}$, where $\lambda_1$ is the smallest…

The graph Cheeger constant and Cheeger inequalities are generalized to the case of hypergraphs whose edges have the same cardinality. In particular, it is shown that the second largest eigenvalue of the generalized normalized Laplacian is…

We study the Cheeger isoperimetric constant as a functional in the space of convex co-compact hyperbolic 3-manifolds which are either quasi-Fuchsian or acylindrical. We prove that the global maximum is attained uniquely at the Fuchsian…

In this article, we prove that typical hyperbolic surfaces, sampled with the Weil-Petersson probability measure, have a spectral gap at least $2/9 - \epsilon$. This is an intermediate result on the way to our proof of the optimal spectral…

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…

We consider a dual Cheeger constant $\overline h$ for finite graphs with edge weights from an arbitrary real-closed ordered field. We obtain estimates of $\overline h$ in terms of number of vertices in graph. Further, we estimate the…

The Cheeger constant of a graph, or equivalently its coboundary expansion, quantifies the expansion of the graph. This notion assumes an implicit choice of a coefficient group, namely, $\mathbb{F}_2$. In this paper, we study Cheeger-type…

For any $\varepsilon>0$, we construct a closed hyperbolic surface of genus $g=g(\varepsilon)$ with a set of at most $\varepsilon g$ systoles that fill, meaning that each component of the complement of their union is contractible. This…

Random hyperbolic graphs have been suggested as a promising model of social networks. A few of their fundamental parameters have been studied. However, none of them concerns their spectra. We consider the random hyperbolic graph model as…