Related papers: Length statistics of random multicurves on closed …
We prove the first polynomial bound on the number of monotonic homotopy moves required to tighten a collection of closed curves on any compact orientable surface, where the number of crossings in the curve is not allowed to increase at any…
The aim of the present paper is to study the distributions of the length multiplicities for negatively curved locally symmetric Riemannian manifolds. In Theorem 2.1, we give upper bounds of the length multiplicities and the square sums of…
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…
We develop a theory for distributed branch points and investigate their role in determining the shape and influencing the mechanics of thin hyperbolic objects. We show that branch points are the natural topological defects in hyperbolic…
In this paper we study the asymptotic behaviour under dilations of probability measures supported on polynomial curves in nilmanifolds. We prove, under some mild conditions, effective equidistribution of such measures to the Haar measure.…
Let $S_g$ be a closed surface of genus $g$ and $\mathcal{H}_g$ be the moduli space of Abelian differentials on $S_g$. A stratum of $\mathcal{H}_g$, endowed with the Masur-Veech measure, becomes a probability space. Then the number of closed…
In this work we present a study on the characterization of ordered and disordered hyperuniform point distributions on spherical surfaces. In spite of the extensive literature on disordered hyperuniform systems in Euclidean geometries, to…
We consider one-dimensional hyperbolic PDEs, linear and nonlinear, with random initial data. Our focus is the {\em pointwise statistics,} i.e., the probability measure of the solution at any fixed point in space and time. For linear…
This work develops a dynamic homogenization approach for metamaterials. It finds an approximate macroscopic homogenized equation with constant coefficients posed in space and time; however, the resulting homogenized equation is higher order…
An analytical theory for the random close packing density, $\phi_\textrm{RCP}$, of polydisperse hard disks is provided using an equilibrium model of crowding [A. Zaccone, Phys. Rev. Lett. 128, 028002 (2022)] which has been justified on the…
In this paper we study the regularized analytic torsion of finite volume hyperbolic manifolds. We consider sequences of coverings $X_i$ of a fixed hyperbolic orbifold $X_0$. Our main result is that for certain sequences of coverings and…
In this paper we continue the analysis of non-diagonalisable hyperbolic systems initiated in \cite{GarJRuz, GarJRuz2}. Here we assume that the system has discontinuous coefficients or more in general distributional coefficients.…
Lateral diffusion of molecules on surfaces plays a very important role in various biological processes, including lipid transport across the cell membrane, synaptic transmission and other phenomena such as exo- and endocytosis, signal…
The goal of the article is to provide different explicit quantifications of the non density of simple closed geodesics on hyperbolic surfaces. In particular, we show that within any embedded metric disk on a surface, lies a disk of radius…
In this paper, we construct and analyze a multiscale (finite element) method for parabolic problems with heterogeneous dynamic boundary conditions. As origin, we consider a reformulation of the system in order to decouple the discretization…
We investigate the terms arising in an identity for hyperbolic surfaces proved by Luo and Tan, namely showing that they vary monotonically in terms of lengths and that they verify certain convexity properties. Using these properties, we…
Hyperbolic propagation offers exciting opportunities in nanophotonics, from sub-diffraction imaging to enhanced local density of states. This transport regime is typically induced by strong modulation of conductivity, i.e., with alternating…
In a variety of settings we provide a method for decomposing a 3-manifold $M$ into pieces. When the pieces have the appropriate type of hyperbolicity, then the manifold $M$ is hyperbolic and its volume is bounded below by the sum of the…
We study the uniqueness of horospheres and equidistant spheres in hyperbolic space under different conditions. First we generalize the Bernstein theorem by Do Carmo and Lawson to the embedded hypersurfaces with constant higher order mean…
We give a short determination of the distribution of the number of $\F_q$-rational points on a random trigonal curve over $\F_q$, in the limit as the genus of the curve goes to infinity. In particular, the expected number of points is…