On length spectrum metrics and weak metrics on Teichmüller spaces of surfaces with boundary

We define and study metrics and weak metrics on the Teichmüller space of a surface of topologically finite type with boundary. These metrics and weak metrics are associated to the hyperbolic length spectrum of simple closed curves and of properly embedded arcs in the surface. We give a comparison between the defined metrics on regions of Teichmüller space which we call $\varepsilon_0$-relative $\epsilon$-thick parts} for $\epsilon >0$ and $\varepsilon_0\geq \epsilon>0$

THE CAPITAL STRUCTURE OF COMPANIES LISTED IN THE GREEK STOCK EXCHANGE

The paper’s aim is to review the capital structure theories, and especially signalling theory. It investigates whether the capital structure signalling theory is reliable in cases of companies listed at the Athens Stock Exchange. The companies used in the sample, raised new equity from 2004 until 2006, and the paper examines their stock price reaction to the announcement.Capital structure, signalling theory

On local comparison between various metrics on Teichmüller spaces

International audienceThere are several Teichmüller spaces associated to a surface of infinite topological type, after the choice of a particular basepoint ( a complex or a hyperbolic structure on the surface). These spaces include the quasiconformal Teichmüller space, the length spectrum Teichmüller space, the Fenchel-Nielsen Teichmüller space, and there are others. In general, these spaces are set-theoretically different. An important question is therefore to understand relations between these spaces. Each of these spaces is equipped with its own metric, and under some hypotheses, there are inclusions between these spaces. In this paper, we obtain local metric comparison results on these inclusions, namely, we show that the inclusions are locally bi-Lipschitz under certain hypotheses. To obtain these results, we use some hyperbolic geometry estimates that give new results also for surfaces of finite type. We recall that in the case of a surface of finite type, all these Teichmüller spaces coincide setwise. In the case of a surface of finite type with no boundary components (and possibly with punctures), we show that the restriction of the identity map to any thick part of Teichmüller space is globally bi-Lipschitz with respect to the length spectrum metric and the classical Teichmüller metric on the domain and on the range respectively. In the case of a surface of finite type with punctures and boundary components, there is a metric on the Teichmüller space which we call the arc metric, whose definition is analogous to the length spectrum metric, but which uses lengths of geodesic arcs instead of lengths of closed geodesics. We show that the restriction of the identity map restricted to any ``relative thick" part of Teichmüller space is globally bi-Lipschitz, with respect to any of the three metrics: the length spectrum metric, the Teichmüller metric and the arc metric on the domain and on the range

Length spectra and the Teichmüller metric for surfaces with boundary

International audienceWe consider some metrics and weak metrics defined on the Teichmmüller space of a surface of finite type with nonempty boundary, that are defined using the hyperbolic length spectrum of simple closed curves and of properly embedded arcs, and we compare these metrics and weak metrics with the Teichmüller metric. The comparison is on subsets of Teichmüller space which we call ''$\varepsilon_0$-relative $\epsilon$-thick parts", and whose definition depends on the choice of some positive constants $\varepsilon_0$ and $\epsilon$. Meanwhile, we give a formula for the Teichmüller metric of a surface with boundary in terms of extremal lengths of families of arcs

A theory of solar type 3 radio bursts

Energetic electrons propagating through the interplanetary medium are shown to excite the one dimensional oscillating two stream instability (OTSI). The OTSI is in turn stabilized by anomalous resistivity which completes the transfer of long wavelength Langmuir waves to short wavelengths, out of resonance with the electrons. The theory explains the small energy losses suffered by the electrons in propagating to 1 AU, the predominance of second harmonic radiation, and the observed correlation between radio and electron fluxes

Nonlinear stability of solar type 3 radio bursts. 1: Theory

A theory of the excitation of solar type 3 bursts is presented. Electrons initially unstable to the linear bump-in-tail instability are shown to rapidly amplify Langmuir waves to energy densities characteristic of strong turbulence. The three-dimensional equations which describe the strong coupling (wave-wave) interactions are derived. For parameters characteristic of the interplanetary medium the equations reduce to one dimension. In this case, the oscillating two stream instability (OTSI) is the dominant nonlinear instability, and is stablized through the production of nonlinear ion density fluctuations that efficiently scatter Langmuir waves out of resonance with the electron beam. An analytical model of the electron distribution function is also developed which is used to estimate the total energy losses suffered by the electron beam as it propagates from the solar corona to 1 A.U. and beyond