163 Result(s)
within
Hyperbolic Geometry
Mathematics
-
Article
Open AccessInversion maps and torus actions on rational homogeneous varieties
Complex projective algebraic varieties with \({{\mathbb {C}}}^*\) ...
-
Article
Open AccessRigidity of geometric structures
Geometric structures on a manifold M arise from a covering of M by charts with values in a homogeneous space G/H, with chart transitions restrictions of elements of G. If M is aspherical, then such geometric stru...
-
Article
Open AccessDivergence of separated nets with respect to displacement equivalence
We introduce a hierarchy of equivalence relations on the set of separated nets of a given Euclidean space, indexed by concave increasing functions ...
-
Article
Open AccessOrthogonal ring patterns in the plane
We introduce orthogonal ring patterns consisting of pairs of concentric circles generalizing circle patterns. We show that orthogonal ring patterns are governed by the same equation as circle patterns. For eve...
-
Article
Open AccessHolomorphic differential forms on moduli spaces of stable curves
We prove that the space of holomorphic p-forms on the moduli space \(\overline{\mathcal {M}}_{g,n}\) ...
-
Article
Open AccessCat(0) polygonal complexes are 2-median
Median spaces are spaces in which for every three points the three intervals between them intersect at a single point. It is well known that rank-1 affine buildings are median spaces, but by a result of Haette...
-
Article
Open AccessConstructions of homotopy 4-spheres by pochette surgery
The boundary sum of the product of a circle with a 3-ball and the product of a disk with a 2-sphere is called a pochette. Pochette surgery, which was discovered by Iwase and Matsumoto, is a generalization of G...
-
Article
Open Access“Lion–man” game and the fixed point property in Hilbert spaces
The main goal of the paper is to show that in the setting of a Hilbert space a closed and convex K has the fixed point property for nonexpansive map**s if and only if the lion always wins the Lion–Man game play...
-
Article
Open AccessOn the entropy of Hilbert geometries of low regularities
We compare the regularity of the boundary of a convex set with the value of its Finslerian volume entropy. The main result states that the volume entropy of a two-dimensional domain whose associated curvature ...
-
Article
Open AccessTotal torsion of three-dimensional lines of curvature
A curve \(\gamma \) γ in a Riemannian manifold M is three-dimensional if it...
-
Article
Open AccessA multiplicity estimate for the Jacobi operator of a nonflat Yang–Mills field over \(\mathbb {S}^m\)
Here we provide refinements of the stability results of Simons and **n, concerning the stability of Yang–Mills fields and harmonic maps respectively. The result also implies the earlier Morse index estimates f...
-
Article
Open AccessThe minimal genus problem for right angled Artin groups
We investigate the minimal genus problem for the second homology of a right angled Artin group (RAAG). Firstly, we present a lower bound for the minimal genus of a second homology class, equal to half the rank...
-
Article
Open AccessTriangulations of grassmannians and flag manifolds
MacPherson (in: Topological methods in modern mathematics: a symposium in Honor of John Milnor’s Sixtieth Birthday Stony Brook NY 1991, Perish, Houston, 1993. https://doi.org/10.2307/1970177
-
Article
Open AccessSemi-simple actions of the Higman-Thompson groups \(T_n\) on finite-dimensional CAT(0) spaces
In this paper, we study isometric actions on finite-dimensional CAT(0) spaces for the Higman–Thompson groups \(T_n\) ...
-
Article
Open AccessConstructing lattice surfaces with prescribed Veech groups: an algorithm
The Veech group of a translation surface is the group of Jacobians of orientation-preserving affine automorphisms of the surface. We present an algorithm which constructs all translation surfaces with a given ...
-
Article
Open AccessHurwitz–Ran spaces
Given a couple of subspaces \({\mathcal {Y}}\subset {\mathcal {X}}\) Y ...
-
Article
Open AccessA compactification of the moduli space of multiple-spin curves
We construct a smooth Deligne–Mumford compactification for the moduli space of curves with an m-tuple of spin structures using line bundles on quasi-stable curves as limiting objects, as opposed to line bundles o...
-
Article
Open AccessGroups of convex bodies
In this paper we introduce and study a topological abelian group of convex bodies, analogous to the scissors congruence group and McMullen’s polytope algebra, with the universal property that continuous valuat...
-
Article
Open AccessRight-angled Coxeter groups with totally disconnected Morse boundaries
This paper introduces a new class of right-angled Coxeter groups with totally disconnected Morse boundaries. We construct this class recursively by examining how the Morse boundary of a right-angled Coxeter gr...
-
Article
Open AccessUniform distribution of saddle connection lengths in all \(\textsf{SL}(2,\pmb {\mathbb {R}})\) orbits
For every flat surface, almost every flat surface in its \(\textsf{SL}(2,\mathbb {R})\) ...
