Related papers: Critical exponent for geodesic currents

Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…

We consider the bond percolation problem on a transient weighted graph induced by the excursion sets of the Gaussian free field on the corresponding cable system. Owing to the continuity of this setup and the strong Markov property of the…

With the use of thermodynamics and general equilibrium conditions only, we study the entropy of a fluid in the vicinity of the critical point of the liquid-vapor phase transition. By assuming a general form for the coexistence curve in the…

Magnetic geodesics describe the trajectory of a particle in a Riemannian manifold under the influence of an external magnetic field. In this article, we use the heat flow method to derive existence results for such curves. We first…

The geodesic equation encodes test-particle dynamics at arbitrary gravitational coupling, hence retaining all orders in the post-Minkowskian (PM) expansion. Here we explore what geodesic motion can tell us about dynamical scattering in the…

Given a Riemannian metric on the 2-sphere, sweep the 2-sphere out by a continuous one-parameter family of closed curves starting and ending at point curves. Pull the sweepout tight by, in a continuous way, pulling each curve as tight as…

For a proper, Gromov-hyperbolic metric space and a discrete, non-elementary, group of isometries, we define a natural subset of the limit set at infinity of the group called the ergodic limit set. The name is motivated by the fact that…

The geodesic structure is very closely related to the trace of the Laplace operator, involved in the calculation of the expectation value of the energy momentum tensor in Universes with non trivial topology. The purpose of this work is to…

In this article we exhibit the largest constant in a quadratic isoperimetric inequality which ensures that a geodesic metric space is Gromov hyperbolic. As a particular consequence we obtain that Euclidean space is a borderline case for…

In this talk a sufficient condition for a diagonal orthogonally transitive cylindrical $G_2$ metric to be geodesically complete is given. The condition is weak enough to comprise all known diagonal perfect fluid cosmological models that are…

The critical behavior at a corner in two-dimensional Ising and three-state Potts models is studied numerically on the square lattice using transfer operator techniques. The local critical exponents for the magnetization and the energy…

We construct a category of examples of partially hyperbolic geodesic flows which are not Anosov, deforming the metric of a compact locally symmetric space of nonconstant negative curvature. Candidates for such example as the product metric…

With inspiration from the K\"ahler geometry, we introduce a metric structure on the energy class, $\mathcal{E}_{1,m}$, of $m$-subharmonic functions with bounded energy and show that it is complete. After studying how the metric convergence…

Let $\Sigma$ be a closed orientable hyperbolic surface. We introduce the notion of a \textit{geodesic current with corners} on $\Sigma$, which behaves like a geodesic current away from certain singularities (the "corners"). We topologize…

Coarse geometry studies metric spaces on the large scale. The recently introduced notion of coarse entropy is a tool to study dynamics from the coarse point of view. We prove that all isometries of a given metric space have the same coarse…

We give a formula for the topological pressure of the geodesic flow of a compact rank 1 manifold in terms of the growth of the number of closed hyperbolic (rank 1) geodesics. We derive an equidistribution result for these geodesics with…

In this paper the magnetic geodesic flow on a 2-torus is considered. We study a semi-hamiltonian quasi-linear PDEs which is equivalent to the existence of polynomial in momenta first integral of magnetic geodesic flow on fixed energy level.…

We show the equivalences of several notions of entropy, like a version of the topological entropy of the geodesic flow and the Minkowski dimension of the boundary, in metric spaces with convex geodesic bicombings satisfying a uniform…

We study numerically the motion of vortices in two-dimensional arrays of resistively shunted Josephson junctions. An extra vortex is created in the ground states by introducing novel boundary conditions and made mobile by applying external…

The motion of a rigid body immersed in an incompressible perfect fluid which occupies a three- dimensional bounded domain have been recently studied under its PDE formulation. In particular classical solutions have been shown to exist…