Related papers: Bounding surface actions on hyperbolic spaces

We obtain bounds for the Faltings's delta function for any Riemann surface of genus greater than one. The bounds are in terms of the genus of the surface and two basic quantities coming from hyperbolic geometry: The length of the shortest…

On a finite-volume hyperbolic $3$-manifold, we establish an upper bound on the area of closed embedded surfaces with constant mean curvature at least one, depending on the mean curvature and the genus bounds. This area bound implies…

In this paper we obtain a bound on the number of isometry classes of finite area hyperbolic surfaces which are length isospectral to a given surface depending only on the topological type of the surface and the length of the shortest closed…

In this article we explore the relationship between the systole and the diameter of closed hyperbolic orientable surfaces. We show that they satisfy a certain inequality, which can be used to deduce that their ratio has a (genus dependent)…

We give sharp upper bounds on the injectivity radii of complete hyperbolic surfaces of finite area with some geodesic boundary components. The given bounds are over all such surfaces with any fixed topology; in particular, boundary lengths…

Looking to the fundamental domains of space groups we can investigate in which space they can be realized. If this space is hyperbolic, then the corresponding space group is also hyperbolic. In addition to the usual methods for…

In this paper, we show that if a group acts isometrically on a good hyperbolic space of finite volume entropy through a non-elementary action, then it admits an affine action on some $L^p$ -space with an unbounded orbit for sufficiently…

We show there is an upper bound on the diameter of a closed, hyperbolic 3-manifold in terms of the length of any presentation of its fundamental group.

We show that word-hyperbolic groups satisfy linear isoperimetric functions for all homotopy types of surface diagrams. This generalises the linear isoperimetric functions for disc and annular diagrams.

The classification of finite group-actions on closed surfaces of small genus is well-known. In the present paper we are interested in the question of which of these group-actions are bounding (extend to a compact 3-manifold with the surface…

We study the number and the length of systoles on complete finite area orientable hyperbolic surfaces. In particular, we prove upper bounds on the number of systoles that a surface can have (the so-called kissing number for hyperbolic…

We address the question of determining which mapping class groups of infinite-type surfaces admit nonelementary continuous actions on hyperbolic spaces. More precisely, let $\Sigma$ be a connected, orientable surface of infinite type with…

It is well known that a hyperbolic domain in the complex plane has uniformly perfect boundary precisely when the product of its hyperbolic density and the distance function to its boundary has a positive lower bound. We extend this…

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…

We consider the problem of when a closed orientable hyperbolic surface admits a totally geodesic embedding into a closed orientable hyperbolic 3-manifold; given a finite isometric group action on the surface, we consider in particular…

We give sharp upper bounds on the maximal injectivity radius of finite-area hyperbolic surfaces and use them, for each g at least 2, to identify a constant r_{g-1,2} with the property that the set of closed genus-g hyperbolic surfaces with…

The goal of this paper is to exhibit and analyze an algorithm that takes a given closed orientable hyperbolic surface and outputs an explicit Dirichlet domain. The input is a fundamental polygon with side pairings. While grounded in…

We prove an inequality bounding the renormalized area of a complete minimal surface in hyperbolic space in terms of the conformal length of its ideal boundary.

We classify the boundaries of hyperbolic groups that have enough quasiconvex codimension-1 surface subgroups with trivial or cyclic intersections.

The Helfrich model is a fundamental tool for determining the morphology of biological membranes. We relate the geometry of an important class of its equilibria to the geometry of sessile and pendant drops in the hyperbolic space ${\bf…