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

On the inclusion of the quasiconformal Teichmüller space into the length-spectrum Teichmüller space

This paper is about surfaces of infinite topological type. Unlike the case of surfaces of finite type, there are several deformation spaces associated with a surface S of infinite topological type. Such spaces depend on the choice of a basepoint (that is, the choice of a fixed conformal structure or hyperbolic structure on S) and they also depend on the choice of a distance on the set of equivalence classes of marked hyperbolic structures. We address the question of the comparison between two deformation spaces, namely, the quasiconformal Teichmüller space and the length-spectrum Teichmüller space. There is a natural inclusion map of the quasiconformal space into the length-spectrum space, which is not always surjective. We work under the hypothesis that the basepoint (a hyperbolic surface) satisfies a condition we call “upper-boundedness”. This means that this surface admits a pants decomposition defined by curves whose lengths are bounded above. The theory under this upper- boundedness hypothesis shows a dichotomy. On the one hand there are surfaces satisfying what we call Shiga’s condition, i.e. they admit a pants decomposition defined by curves whose lengths are bounded above and below. If the base point satisfies Shiga’s condition, then the inclusion of the quasiconformal space into the length- spectrum space is surjective, and it is a homeomorphism. In this paper we concentrate on the other kind of upper-bounded surfaces, which we call “upper-bounded with short interior curves”. This means that the corresponding hyperbolic surface admits a pants decomposition defined by curves whose lengths are bounded above, and such that the lengths of some interior curves approach zero. We show that in this case the behavior is completely different. Under this hypothesis, the image of the inclusion between the two Teichmüller spaces is nowhere dense in the length-spectrum space. As a corollary of the methods used, we obtain an explicit parametrization of the length-spectrum Teichmüller space in terms of Fenchel–Nielsen coordinates and we prove that the length-spectrum Teichmüller space is path-connected

Path integral evaluation of Dbrane amplitudes

We extend Polchinski's evaluation of the measure for the one-loop closed string path integral to open string tree amplitudes with boundaries and crosscaps embedded in Dbranes. We explain how the nonabelian limit of near-coincident Dbranes emerges in the path integral formalism. We give a careful path integral derivation of the cylinder amplitude including the modulus dependence of the volume of the conformal Killing group.Comment: Extended version replacing hep-th/9903184, includes discussion of nonabelian limit, Latex, 10 page

Scattering of Glueballs and Mesons in Compact QEDQED in 2+12+1 Dimensions

We study glueball and meson scattering in compact $QED_{2+1}$ gauge theory in a Hamiltonian formulation and on a momentum lattice. We compute ground state energy and mass, and introduce a compact lattice momentum operator for the computation of dispersion relations. Using a non-perturbative time-dependent method we compute scattering cross sections for glueballs and mesons. We compare our results with strong coupling perturbation theory.Comment: figures not included (hard copy only), LAVAL-PHY-94-05, PARKS-PHY-94-0

Cerebral plasticity in acute vestibular deficit

The aim of this study was to analyze the effect of acute vestibular deficit on the cerebral cortex and its correlation with clinical signs and symptoms. Eight right-handed patients affected by vestibular neuritis, a purely peripheral vestibular lesion, underwent two brain single photon emission computed tomography (SPECT) in 1 month. The first SPECT analysis revealed reduced blood flow in the temporal frontal area of the right hemisphere in seven of eight patients, independent of the right/left location of the lesion. The alteration was present always in the right, non-dominant hemisphere and was reversible in some patients 1 month after the onset, together with attenuation of signs and symptoms. It may be hypothesized that the transient reduction of cortical blood flow and subsequently of cortical activity in the non-dominant hemisphere, also the expression of cerebral plasticity, may serve as a defense mechanism aimed to attenuate the vertigo symptom

A vanadium / aspirin complex controlled release using a poly(ß-propiolactone) lm.

A delivery system for vanadiumwas developed using poly(¯-propiolactone)(P¯PL) lms. The release kinetics of a complex of vanadium (IV) with aspirin (VOAspi) was evaluated with lms prepared from polymers of differentmolecularweights, as well as with variable drug load. A sustained release of vanadium over 7 days was achieved. The drug release kinetics depends on contributions from two factors: (a) diffusion of the drug; and (b) erosion of the P¯PL lm. The experimental data at an early stage of release were tted with a diffusion model, which allowed determination of the diffusion coef cient of the drug. VOAspi does not show strong interaction with the polymer, as demonstrated by the low apparent partition coef cient (approximately 10¡2). UMR106 osteosarcoma cells were used as a model to evaluate the anticarcinogenic effects of the VOAspi released from the P¯PL lm. VOAspi–P¯PL lm inhibited cell proliferation in a dose-response manner and induced formation of approximately half of the thiobarbituric acid reactive substances (TBARS), an index of lipid peroxidation, compared to that with free VOAspi in solution. The unloaded P¯PL lm did not generate cytotoxicity, as evaluated by cell growth and TBARS. Thus, the polymer-embedded VOAspi retained the antiproliferative effects showing lower cytotoxicity than the free drug. Results with VOAspi–P¯PL lms suggest that this delivery system may have promising biomedical and therapeutic applications

Adhesion mechanisms of the contact interface of TiO2 nanoparticles in films and aggregates

Fundamental knowledge about the mechanisms of adhesion between oxide particles with diameters of few nanometers is impeded by the difficulties associated with direct measurements of contact forces at such a small size scale. Here we develop a strategy based on AFM force spectroscopy combined with all-atom molecular dynamics simulations to quantify and explain the nature of the contact forces between 10 nm small TiO2 nanoparticles. The method is based on the statistical analysis of the force peaks measured in repeated approaching/retracting loops of an AFM cantilever into a film of nanoparticle agglomerates and relies on the in-situ imaging of the film stretching behavior in an AFM/TEM setup. Sliding and rolling events first lead to local rearrangements in the film structure when subjected to tensile load, prior to its final rupture caused by the reversible detaching of individual nanoparticles. The associated contact force of about 2.5 nN is in quantitative agreement with the results of molecular dynamics simulations of the particle–particle detachment. We reveal that the contact forces are dominated by the structure of water layers adsorbed on the particles’ surfaces at ambient conditions. This leads to nonmonotonous force–displacement curves that can be explained only in part by classical capillary effects and highlights the importance of considering explicitly the molecular nature of the adsorbates

The stability for the Cauchy problem for elliptic equations

We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality.Comment: 57 pages, review articl