Related papers: Large hyperbolic circles
Inspired by [6, 7], we study the boundary regularity of constant curvature hypersurfaces in the hyperbolic space $\mathbb{H}^{n+1}$, which have prescribed asymptotic boundary at infinity. Through constructing the boundary expansions of the…
In this paper we develope a quantitative non-divergence theorem for translates of horospherical orbits, using the technique of Margulis' inequality as developed by Eskin-Margulis-Mozes and Eskin-Margulis. As we use the Margulis' inequality,…
We provide a formula to compute the volume of the intersection of a generalized cylinder with a hyperplane. Then we prove an integral inequality involving Bessel functions similar to Keith Ball's well-known inequality. Using this inequality…
We prove an effective equidistribution result for periodic orbits of semisimple groups on congruence quotients of an ambient semisimple group. This extends previous work of Einsiedler, Margulis and Venkatesh. The main new feature is that we…
The main results of this paper are limit theorems for horocycle flows on compact surfaces of constant negative curvature. One of the main objects of the paper is a special family of horocycle-invariant finitely-additive Hoelder measures on…
Let P be a locally finite circle packing in the plane invariant under a non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When Gamma is geometrically finite, we construct an explicit Borel measure on the plane which…
Our main result is that for all sufficiently large $x_0>0$, the set of commensurability classes of arithmetic hyperbolic 2- or 3-orbifolds with fixed invariant trace field $k$ and systole bounded below by $x_0$ has density one within the…
This paper contains theory on two related topics relevant to manifolds of normally hyperbolic singularities. First, theorems on the formal and $ C^k $ normal forms for these objects are proved. Then, the theorems are applied to give…
For compact Riemann surfaces, the collar theorem and Bers' partition theorem are major tools for working with simple closed geodesics. The main goal of this paper is to prove similar theorems for hyperbolic cone-surfaces. Hyperbolic…
Using the works of Ma\~n\'e \cite{Ma} and Paternain \cite{Pat} we study the distribution of geodesic arcs with respect to equilibrium states of the geodesic flow on a closed manifold, equipped with a $\mathcal{C}^{\infty}$ Riemannian…
We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds…
We study the problem of propagation of analytic regularity for semi-linear symmetric hyperbolic systems. We adopt a global perspective and we prove that if the initial datum extends to a holomorphic function in a strip of radius (=width)…
Let $\varphi_t : M \to M$ be a flow on a smooth closed connected manifold $M$ that preserves and expands a foliation $F$. We establish a theorem of propagation of regularity along the leaves of $F$ for sections of vector bundles satisfying…
We investigate the scalar-wave resonances of systems composed of identical Neumann-type inclusions arranged periodically around a circular ring. Drawing on natural similarities with the undamped Rayleigh-Bloch waves supported by infinite…
In this work we treat a famous topic in Ergodic Theory and Dynamical Systems: uniformly expanding maps. We relate regularity of expanding maps and conjugacies with Lyapunov exponents, metric and topological entropies for expanding maps of…
The dynamics of thin, non-circular droplets evaporating in the diffusion-limited regime are examined. The challenging non-rectilinear mixed-boundary problem this poses is solved using a novel asymptotic approach and an asymptotic expansion…
We sketch the proof of an effective equidistribution theorem for one-parameter unipotent subgroups in $S$-arithmetic quotients arising from $\mathbf K$-forms of $\mathrm{SL}_2^{\mathsf n}$ where $\mathbf K$ is a number field. This gives an…
A method is described to sum multi-dimensional arithmetic functions subject to hyperbolic summation conditions, provided that asymptotic formulae in rectangular boxes are available. In combination with the circle method, the new method is a…
We observe that a large part of the volume of a hyperbolic polyhedron is taken by a tubular neighbourhood of its boundary, and use this to give a new proof for the finiteness of arithmetic maximal reflection groups following a recent work…
We strongly develop the relationship between complex hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on complex hyperbolic spaces, especially in dimension $2$.…