Related papers: Goldberg's constants
A basic feature of Teichm\"uller theory of Riemann surfaces is the interplay of two dimensional hyperbolic geometry, the behavior of geodesic-length functions and Weil-Petersson geometry. Let $\mathcal{T}_g$ $(g\geq 2)$ be the Teichm\"uller…
In this paper, we study the extremal problem for the Strichartz inequality for the Schr\"{o}dinger equation on the $\mathbb{R} \times \mathbb{R}^2$; we provide a new proof to the characterization of the extremal functions. The only extremal…
The ultimate goal of our book is to present a unified approach to the dynamics, ergodic theory, and geometry of elliptic functions from $\C$ to $\oc$. We consider elliptic functions as a most regular class of transcendental meromorphic…
We establish the dual notions of scaling and saturation from geometric control theory in an infinite-dimensional setting. This generalization is applied to the low-mode control problem in a number of concrete nonlinear partial differential…
This paper is concerned with Kolmogorov's two-equation model for the free turbulence in three dimensions. We first discuss scaling laws for slightly more general two-equation models to highlight the special role of the model devised by…
The theory of finitely generated relative (co)tilting modules has been established in the 1980s by Auslander and Solberg, and infinitely generated relative tilting modules have recently been studied by many authors in the context of…
Moduli spaces of hyperbolic surfaces with geodesic boundary components of fixed lengths may be endowed with a symplectic structure via the Weil-Petersson form. We show that, as the boundary lengths are sent to infinity, the Weil-Petersson…
Let $f$ be an arbitrary integrable function on a finite measure space $(X,\Sigma, \nu)$. We characterise the extreme points of the set $\Omega (f)$ of all measurable functions on $(X,\Sigma, \nu)$ majorised by $f$, providing a complete…
Formulas for the solutions of initial value problems for ordinary differential equations with singular $\delta^{(n)}$-like driving terms are derived in the framework of an algebra of generalized functions (of Colombeau type) over a field of…
In this talk we shall show a perfect fluid cosmological model and its properties. The model possesses an orthogonally transitive abelian two-dimensional group of isometries that corresponds to cylindrical symmetry. The matter content is a…
Recent work by the authors led to the development of a mathematical theory dealing with `second--order hyperbolic Fuchsian systems', as we call them. In the present paper, we adopt a physical standpoint and discuss the implications of this…
We present a careful approximation of the geodesics in trees of hyperbolic or relatively hyperbolic groups. As an application we prove a combination theorem for finite graphs of relatively hyperbolic groups, with both Farb's and Gromov's…
We generalize the notion of tight geodesics in the curve complex to tight trees. We then use tight trees to construct model geometries for certain surface bundles over graphs. This extends some aspects of the combinatorial model for doubly…
An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…
We consider continuous maps $f:X\to X$ on compact metric spaces admitting inducing schemes of hyperbolic type introduced in [15] as well as the induced maps $\tilde{f}:\tilde{X}\to\tilde{X}$ and the associated tower maps $\hat{f}:\hat{X}…
The Green functions were first introduced by Green to compute the character table of GLn(q) in 1955. They were later generalized by Deligne and Lusztig for an arbitrary finite group of Lie type G(q) using l-adic cohomological methods…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
We give an introduction to the realisation theory for infinite-dimensional systems. That is, we show that for any function $G$, analytic and bounded in the right half of the complex plane, there exists operators $A,B,C$ such that…
Geometric methods proposed by Stallings for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups. It turns out that Stallings'…
In this paper, we discuss the approximate controllability for control systems governed by stochastic evolution hemivariational inequalities in Hilbert spaces. The interest in studying this type of equation comes from its application in some…