Thurston's metric on Teichm\"uller space and the translation lengths of mapping classes

We show that the Teichm\"uller space of a surface without boundary and with punctures, equipped with Thurston's metric is the limit (in an appropriate sense) of Teichm\"uller spaces of surfaces with boundary, equipped with their arc metrics, when the boundary lengths tend to zero. We use this to obtain a result on the translation distances for mapping classes for their actions on Teichm\"uller spaces equipped with their arc metrics

Solitons in (1,1)-supersymmetric massive sigma model

We find the solitons of massive (1,1)-supersymmetric sigma models with target space the groups $SO(2)$ and $SU(2)$ for a class of scalar potentials and compute their charge, mass and moduli space metric. We also investigate the massive sigma models with target space any semisimple Lie group and show that some of their solitons can be obtained from embedding the $SO(2)$ and $SU(2)$ solitons.Comment: Phyzzx.tex, 32 pp, 3 fig

Quasiconformal mappings, from Ptolemy's geography to the work of Teichmüller

The origin of quasiconformal mappings, like that of conformal mappings, can be traced back to old cartography where the basic problem was the search for mappings from the sphere onto the plane with minimal deviation from conformality, subject to certain conditions which were made precise. In this paper, we survey the development of cartography, highlighting the main ideas that are related to quasiconformality. Some of these ideas were completely ignored in the previous historical surveys on quasiconformal mappings. We then survey early quasiconformal theory in the works of Grötzsch, Lavrentieff, Ahlfors and Teichmüller, which are the 20th-century founders of the theory

Spacecraft-induced plasma energization and its role in flow phenomena

Plasma instabilities induced by orbiting vehicles can cause many important phenomena ranging from electron and ion heating and suprathermal electron tail energization, to enhanced ionization and optical emissions. We outline the basic collective processes leading to plasma energization near plasma sheaths and in regions of neutral gas streaming through plasma, and discuss the role of the induced collective effects in producing the optical emission spectra

Some Lipschitz maps between hyperbolic surfaces with applications to Teichmüller theory

International audienceIn the Teichmüller space of a hyperbolic surface of finite type, we construct geodesic lines for Thurston's asymmetric metric having the property that when they are traversed in the reverse direction, they are also geodesic lines (up to reparametrization). The lines we construct are special stretch lines in the sense of Thurston. They are directed by complete geodesic laminations that are not chain-recurrent, and they have a nice description in terms of Fenchel-Nielsen coordinates. At the basis of the construction are certain maps with controlled Lipschitz constants between right-angled hyperbolic hexagons having three non-consecutive edges of the same size. Using these maps, we obtain Lipschitz-minimizing maps between hyperbolic particular pairs of pants and, more generally, between some hyperbolic sufaces of finite type with arbitrary genus and arbitrary number of boundary components. The Lipschitz-minimizing maps that we contruct are distinct from Thurston's stretch maps

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 $\varepsilon_0\geq \epsilon>0$