Related papers: Systoles in translation surfaces

A translational surface is a tensor product surface constructed from two space curves by translating one along the other. These surfaces are common within geometric modeling and, since their description is parametric, it is desirable to…

Parallel transport of a connection in a smooth fibre bundle yields a functor from the path groupoid of the base manifold into a category that describes the fibres of the bundle. We characterize functors obtained like this by two notions we…

After having investigated the geodesic and translation triangles and their angle sums in $\SOL$ and $\SLR$ geometries we consider the analogous problem in $\NIL$ space that is one of the eight 3-dimensional Thurston geometries. We analyze…

The aim of this paper is to obtain an asymptotic expansion for ergodic integrals of translation flows on flat surfaces of higher genus (Theorem 1) and to give a limit theorem for these flows (Theorem 2).

We refine the theory of the cohomological equation for translation flows on higher genus surfaces with the goal of proving optimal results on the Sobolev regularity of solutions and of distributional obstructions. For typical translation…

Many contemporary applications in signal processing and machine learning give rise to structured non-convex non-smooth optimization problems that can often be tackled by simple iterative methods quite effectively. One of the keys to…

We consider smooth flows preserving a smooth invariant measure, or, equivalently, locally Hamiltonian flows on compact orientable surfaces and show that, when the genus of the surface is two, almost every such locally Hamiltonian flow with…

We give the formula for the maximal systole of the surface admits the largest $S^3$-extendable abelian group symmetry. The result we get is $2\mathrm{arccosh} K$. Here \begin{eqnarray*} K &=& \sqrt[3]{\frac{1}{216}L^3 +\frac{1}{8} L^2 +…

Given a saddle fixed point of a surface diffeomorphism, its stable and unstable curves $W^S$ and $W^U$ often form a homoclinic tangle. Given such a tangle, we use topological methods to find periodic points of the diffeomorphism, using only…

With any max-stable random process $\eta$ on $\mathcal{X}=\mathbb{Z}^d$ or $\mathbb{R}^d$, we associate a random tessellation of the parameter space $\mathcal{X}$. The construction relies on the Poisson point process representation of the…

We address the problem of optimal transport with a quadratic cost functional and a constraint on the flux through a constriction along the path. The constriction, conceptually represented by a toll station, limits the flow rate across. We…

We consider spatial stochastic models, which can be applied e.g. to telecommunication networks with two hierarchy levels. In particular, we consider two Cox processes concentrated on the edge set of a random tessellation, where the points…

Here we survey on the growth of systoles of arithmetic locally symmetric spaces under the congruence covering and give simple proofs for the best possible constants of Gromov for several important classes of symmetric spaces.

We establish sharp well-posedness and approximation estimates for variational saddle point systems at the continuous level. The main results of this note have been known to be true only in the finite dimensional case. Known spectral results…

The ribosome flow model on a ring (RFMR) is a deterministic model for translation of a circularized mRNA. We derive a new spectral representation for the optimal steady-state production rate and the corresponding optimal steady-state…

Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…

A fundamental problem in the study of complex networks is to provide quantitative measures of correlation and information flow between different parts of a system. To this end, several notions of communicability have been introduced and…

We study a diophantine property for translation surfaces, defined in term of saddle connections and inspired by the classical theorem of Khinchin. We prove that the same dichotomy holds as in Khinchin' result, then we deduce a sharp…

We propose a generalization of the concept of symmetry as a continuous function of the reference center or line location. We suggest that this concept can be applied to many closed systems and exploring its time evolution. When the function…

By studying connectedness at infinity of systolic groups we distinguish them from some other classes of groups, in particular from the fundamental groups of manifolds covered by euclidean space of dimension at least three. We also study…