相关论文: Currents on free groups
Graphene has generated a lot of research interest due to its special properties, which include a hydrodynamic regime. It is not yet clear however which boundary condition such a hydrodynamic current flow satisfies. The aim of this paper is…
We prove a quantitative estimate, with a power saving error term, for the number of simple closed geodesics of length at most $L$ on a compact surface equipped with a Riemannian metric of negative curvature. The proof relies on the…
In this paper we compare the different phenomena that occur when intersecting geometric objects with random geodesics on the unit sphere and inside convex bodies. On the high dimensional sphere we see that with probability bounded away from…
We provide a derivation of several classes of boundary conditions for fluids of Korteweg-type using a simple and transparent thermodynamic approach that automatically guarentees that the derived boundary conditions are compatible with the…
When a shallow layer of inviscid fluid flows over a substrate, the fluid particle trajectories are, to leading order in the layer thickness, geodesics on the two-dimensional curved space of the substrate. Since the two-dimensional geodesic…
This paper is about a type of quantitative density of closed geodesics and orthogeodesics on complete finite-area hyperbolic surfaces. The main results are upper bounds on the length of the shortest closed geodesic and the shortest doubly…
Within the Onsager theory we study free planar isotropic-nematic interfaces in binary mixtures of hard rods. For sufficiently different particle shapes the bulk phase diagrams of these mixtures exhibit a triple point, where an isotropic (I)…
The status of flow in heavy-ion collisions and of inference of hadronic-matter properties is reviewed.
We construct examples of free-by-cyclic hyperbolic groups which fiber in infinitely many ways over Z. The construction involves adding a specialized square 2-cell to a non-positively curved, squared 2-complex defined by labeled oriented…
The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the…
In this paper we study a model of an interface between two fluids in a porous medium. For this model we prove several local and global well-posedness results and study some of its qualitative properties. We also provide numerics.
Let $F_N$ be a free group of rank $N\ge 2$, let $\mu$ be a geodesic current on $F_N$ and let $T$ be an $\mathbb R$-tree with a very small isometric action of $F_N$. We prove that the geometric intersection number $<T, \mu>$ is equal to zero…
We propose a new condition $\aleph$ which enables to get new results on integrable geodesic flows on closed surfaces. This paper has two parts. In the first, we strengthen Kozlov's theorem on non-integrability on surfaces of higher genus.…
We address the existence and of solutions for the Euler-plate free-boundary system modeling an interaction of a three-dimensional inviscid fluid and an evolving plate. We prove the local existence and uniqueness of solutions for initial…
We provide sufficient conditions for two subgroups of a hierarchically hyperbolic group to generate an amalgamated free product over their intersection. The result applies in particular to certain geometric subgroups of mapping class groups…
The geodesic flow on a finite discrete q-manifold with or without boundary is defined as as a permutation of its ordered q-simplices. This allows to define geodesic sheets and a notion of sectional curvature.
Recently it has been argued that autoparallels should be the correct description of free particle motion in spaces with torsion, and that such trajectories can be derived from variational principles if these are suitably adapted. The…
We give bounds on the number of non-simple closed curves on a negatively curved surface, given upper bounds on both length and self-intersection number. In particular, it was previously known that the number of all closed curves of length…
Let $\varphi$ be a hyperbolic outer automorphism of a non-abelian free group $F_N$ such that $\varphi$ and $\varphi^{-1}$ admit absolute train track representatives. We prove that $\varphi$ acts on the space of projectivized geodesic…
I review how hydrodynamical flow is related to the observed flow in ultrarelativistic heavy ion collisions and how initial conditions, equation of state and freeze-out temperature affect flow in hydrodynamical models.