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We provide a corrected proof of a theorem of A. Bellis on strong stable sets in the unit tangent bundle of certain hyperbolic surfaces. The theorem states that, for vectors whose geodesic rays encounter arbitrarily short closed geodesics,…
Parabolic cut pairs in the boundaries of relatively hyperbolic group are a new and previously unexplored phenomenon. In this paper, we give a way to create examples of relatively hyperbolic groups with parabolic cut pairs on their boundary…
The aim of this paper is to investigate the fractional combinatorial Calabi flow for hyperbolic bordered surfaces. By Lyapunov theory, it is proved that the flow exists for all time and converges exponentially to a conformal factor that…
We present a parabolic approximation that incorporates reflection. With this approximation, there is no need to solve the parabolic equation for a coupled pair of solutions consisting of the incident and reflected waves. Rather, this…
We show that, assuming Vojta's height conjecture, the height of a rational point on an algebraically hyperbolic variety can be bounded "uniformly" in families. This generalizes a result of Su-Ion Ih for curves of genus at least two to…
We study the nonresonance phenomenon for complex rank-one local systems on complements of hyperplane arrangements. We refine the method of Cohen, Dimca, and Orlik and obtain a combinatorial sufficient condition for nonresonance. As an…
Coherent state path integrals are applied to a many-body problem for non-relativistic electrons in a central potential and an external magnetic field; however, in comparison to previous coherent state path integrals, we definitely fix the…
We use a variational principle to prove an existence and uniqueness theorem for planar weighted Delaunay triangulations (with non-intersecting site-circles) with prescribed combinatorial type and circle intersection angles. Such weighted…
A new method is developed for solving the conformally invariant integrals that arise in conformal field theories with a boundary. The presence of a boundary makes previous techniques for theories without a boundary less suitable. The method…
In this note, we present a proof of Smarandache's cevian triangle hyperbolic theorem in the Einstein relativistic velocity model of hyperbolic geometry.
We use the probabilistic method to obtain versions of the colorful Carath\'eodory theorem and Tverberg's theorem with tolerance. In particular, we give bounds for the smallest integer $N=N(t,d,r)$ such that for any $N$ points in $R^d$,…
We investigate the discontinuity of codings for the Julia set of a quadratic map. To each parameter ray, we associate a natural coding for Julia sets on the ray. Given a hyperbolic component $H$ of the Mandelbrot set, we consider the…
For a convex domain $D$ that is enclosed by the hypersurface $\partial D$ of bounded normal curvature, we prove an angle comparison theorem for angles between $\partial D$ and geodesic rays starting from some fixed point in $D$, and the…
We develop an efficient and convergent numerical method for solving the inverse problem of determining the potential of nonlinear hyperbolic equations from lateral Cauchy data. In our numerical method we construct a sequence of linear…
We establish the convergence theory of multiplicative Diophantine approximation for all non-degenerate, smooth manifolds. We also settle said convergence theory for all affine subspaces satisfying a highly generic and essentially optimal…
We analyze a real one-parameter family of quasiconformal deformations of a hyperbolic rational map known as {\em spinning}. We show that under fairly general hypotheses, the limit of spinning either exists and is unique, or else converges…
We consider a system of two kinetic equations modelling a multicellular system : The first equation governs the dynamics of cells, whereas the second kinetic equation governs the dynamics of the chemoattractant. For this system, we first…
We construct a Cayley graph $\mathbf{Cay}_S(\Gamma)$ of a hyperbolic group $\Gamma$ such that there are elements $g,h\in\Gamma$ and a point $\gamma \in \partial_\infty\Gamma = \partial_\infty\mathbf{Cay}_S(\Gamma)$ such that the sets…
Under natural assumptions on the observable, we prove a Central Limit Theorem, a Berry-Esseen Theorem, and a quantitative Local Limit Theorem for a broad class of partially hyperbolic endomorphisms of the two-dimensional torus. Our results…
In Euclidean Ramsey Theory usually we are looking for monochromatic configurations in the Euclidean space, whose points are colored with a fixed number of colors. In the canonical version, the number of colors is arbitrary, and we are…