Related papers: Extremal parameters and their duals for Fuchsian b…

This paper explores extremal self-dual double circulant (DC) codes and linear complementary dual (LCD) codes of arbitrary length over the Galois field $\mathbb F_2$. We establish the sufficient and necessary conditions for DC codes and…

In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies with determining which subsets of variables can take…

In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…

Within the Kardar-Parisi-Zhang universality class, the space-time Airy sheet is conjectured to be the canonical scaling limit for last passage percolation models. In recent work arXiv:1812.00309 of Dauvergne, Ortmann, and Vir\'ag, this…

We show the flexibility of the metric entropy and obtain additional restrictions on the topological entropy of geodesic flow on closed surfaces of negative Euler characteristic with smooth non-positively curved Riemannian metrics with fixed…

This continues the investigation of a combinatorial model for the variation of dynamics in the family of rational maps of degree two, by concentrating on those varieties in which one critical point is periodic. We prove some general results…

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.

In this paper we provide a connection between the geometrical properties of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the…

As a final work to establish that frame flows for geometrically finite hyperbolic manifolds of arbitrary dimensions are exponentially mixing with respect to the Bowen-Margulis-Sullivan measure, this paper focuses on the case with cusps. To…

In this paper, several fundamental facts, especially the existence and uniqueness of an absolutely continuous ergodic measure with an exponential mixing rate, are derived for smooth expanding circle maps. Although the results are classical,…

In this paper we study the area function of polygons, where the vertices are sliding along curves. We give geometric criteria for the critical points and determine also the Hesse matrix at those points. This is the starting point for a…

We derive pointwise curvature estimates for graphical mean curvature flows in higher codimensions. To the best of our knowledge, this is the first such estimates without assuming smallness of first derivatives of the defining map. An…

Parametric finite elements lead to very efficient numerical methods for surface evolution equations. We introduce several computational techniques for curvature driven evolution equations based on a weak formulation for the mean curvature.…

This paper consists of two halves. In the first half of the paper, we consider real-valued functions $f$ whose domain is the vertex set of a graph $G$ and that are Lipschitz with respect to the graph distance. By placing a uniform…

This paper develops the geometry and analysis of the averaged Euler equations for ideal incompressible flow in domains in Euclidean space and on Riemannian manifolds, possibly with boundary. The averaged Euler equations involve a parameter…

We investigate typical properties of nonexpansive mappings on unbounded complete hyperbolic metric spaces. For two families of metrics of uniform convergence on bounded sets, we show that the typical nonexpansive mapping is a Rakotch…

The extremal functional method determines approximate solutions to the constraints of crossing symmetry, which saturate bounds on the space of unitary CFTs. We show that such solutions are characterized by extremality conditions, which may…

If the Alday-Maldacena version of string/gauge duality is formulated as an equivalence between double loop and area integrals a la arXiv: 0708.1625, then this pure geometric relation can be tested for various choices of n-side polygons. The…

Structural properties of large random maps and lambda-terms may be gleaned by studying the limit distributions of various parameters of interest. In our work we focus on restricted classes of maps and their counterparts in the…

In [12], the existence of ideal circle patterns in Euclidean or hyperbolic background geometry under the combinatorial conditions was proved using flow approaches. It remains as an open problem for the spherical case. In this paper, we…