相关论文: On hyperbolic fixed points in ultrametric dynamics

Given a metric (graph) bundle $X$ over $B$ where all the fibres are strongly relatively hyperbolic and nonelementary we show that, under certain conditions, $X$ is strongly hyperbolic relative to a collection of maximal cone-subbundles of…

This short review surveys mass for two-dimensional asymptotically locally hyperbolic initial data sets. I explain the difficulties in defining mass in spatial dimension two, which are resolved via minimisation using a positive energy…

We bound two global invariants of cusped hyperbolic manifolds: the length of the shortest closed geodesic (the systole), and the radius of the biggest embedded ball (the inradius). We give an upper bound for the systole, expressed in terms…

Let $\mathcal{P}$ be a packing of circular disks of radius $\rho>0$ in the Euclidean, spherical, or hyperbolic plane. Let $0\leq\lambda\leq\rho$. We say that $\mathcal{P}$ is a $\lambda$-separable packing of circular disks of radius $\rho$…

We establish sufficient conditions for the hyperbolicity of the billiard dynamics on surfaces of constant curvature. This extends known results for planar billiards. Using these conditions, we construct large classes of billiard tables with…

Learning the representation of data with hierarchical structures in the hyperbolic space attracts increasing attention in recent years. Due to the constant negative curvature, the hyperbolic space resembles tree metrics and captures the…

For a hyperbolic fibered 3-manifold M, we prove results that uniformly relate the structure of surface projections as one varies the fibrations of M. This extends our previous work from the fully-punctured to the general case.

Existing theoretical stabilization results for linear, hyperbolic multi-dimensional problems are extended to the discretized multi-dimensional problems. In contrast to existing theoretical and numerical analysis in the spatially…

We investigate the rigidity of hyperbolic cone metrics on $3$-manifolds which are isometric gluing of ideal and hyper-ideal tetrahedra in hyperbolic spaces. These metrics will be called ideal and hyper-ideal hyperbolic polyhedral metrics.…

The zero set of the hyperbolic Gaussian analytic function is a random point process in the unit disc whose distribution is invariant under automorphisms of the disc. We study the variance of the number of points in a disc of increasing…

We extend a recent proof of hyperbolicity of the exact (to all orders in Knudsen number) linear hydrodynamic equations [M. Colangeli et al, Phys. Rev. E (2007), in press; arXiv:cond-mat/0703791v2] to the three-dimensional Grad's moment…

We consider globally hyperbolic maximal anti de Sitter 3-manifolds $M$ with a closed Cauchy surface $S$ of genus greater than one and prove that any pair of hyperbolic metrics on $S$ can be realized as the boundary metrics of the convex…

Representing data in hyperbolic space can effectively capture latent hierarchical relationships. With the goal of enabling accurate classification of points in hyperbolic space while respecting their hyperbolic geometry, we introduce…

We consider the possible sizes of large sumfree sets contained in the discrete hypercube $\{1,...,n\}^k$, and we determine upper and lower bounds for the maximal size as $n$ becomes large. We also discuss a continuous analogue in which our…

The purpose of the present paper is to prove existence of super-exponentially many compact orientable hyperbolic arithmetic $n$-manifolds that are geometric boundaries of compact orientable hyperbolic $(n+1)$-manifolds, for any $n \geq 2$,…

We obtain a exponential large deviation upper bound for continuous observables on suspension semiflows over a non-uniformly expanding base transformation with non-flat singularities and/or discontinuities, where the roof function defining…

Learning generalizable self-supervised graph representations for downstream tasks is challenging. To this end, Contrastive Learning (CL) has emerged as a leading approach. The embeddings of CL are arranged on a hypersphere where similarity…

We develop a ``canonical Wick rotation-rescaling theory in 3-dimensional gravity''. This includes: (a) A simultaneous classification that shows how generic maximal globally hyperbolic spacetimes of constant curvature, which admit a complete…

The study of rod complements is motivated by rod packing structures in crystallography. We view them as complements of links comprised of Euclidean geodesics in the 3-torus. Recent work of the second author classifies when such rod…

In this paper, we show that for several interesting systems beyond uniform hyperbolicity, any generic continuous function has a unique maximizing measure with zero entropy. In some cases, we also know that the maximizing measure has full…