Non-rigidity of spherical inversive distance circle packings

We give a counterexample of Bowers-Stephenson's conjecture in the spherical case: spherical inversive distance circle packings are not determined by their inversive distances.Comment: 6 pages, one pictur

Minimal surfaces and particles in 3-manifolds

We use minimal (or CMC) surfaces to describe 3-dimensional hyperbolic, anti-de Sitter, de Sitter or Minkowski manifolds. We consider whether these manifolds admit ``nice'' foliations and explicit metrics, and whether the space of these metrics has a simple description in terms of Teichm\"uller theory. In the hyperbolic settings both questions have positive answers for a certain subset of the quasi-Fuchsian manifolds: those containing a closed surface with principal curvatures at most 1. We show that this subset is parameterized by an open domain of the cotangent bundle of Teichm\"uller space. These results are extended to ``quasi-Fuchsian'' manifolds with conical singularities along infinite lines, known in the physics literature as ``massive, spin-less particles''. Things work better for globally hyperbolic anti-de Sitter manifolds: the parameterization by the cotangent of Teichm\"uller space works for all manifolds. There is another description of this moduli space as the product two copies of Teichm\"uller space due to Mess. Using the maximal surface description, we propose a new parameterization by two copies of Teichm\"uller space, alternative to that of Mess, and extend all the results to manifolds with conical singularities along time-like lines. Similar results are obtained for de Sitter or Minkowski manifolds. Finally, for all four settings, we show that the symplectic form on the moduli space of 3-manifolds that comes from parameterization by the cotangent bundle of Teichm\"uller space is the same as the 3-dimensional gravity one.Comment: 53 pages, no figure. v2: typos corrected and refs adde

Disorder Effects in the Bipolaron System Ti4_{4}O7_{7} Studied by Photoemission Spectroscopy

We have performed a photoemission study of Ti$_{4}$O$_{7}$ around its two transition temperatures so as to cover the metallic, high-temperature insulating (bipolaron-liquid), and low-temperature insulating (bipolaron-crystal) phases. While the spectra of the low-temperature insulating phase show a finite gap at the Fermi level, the spectra of the high-temperature insulating phase are gapless, which is interpreted as a soft Coulomb gap due to dynamical disorder. We suggest that the spectra of the high-temperature disordered phase of Fe$_{3}$O$_{4}$, which exhibits a charge order-disorder transition (Verwey transition), can be interpreted in terms of a Coulomb gap.Comment: 4 pages, 3 epsf figures embedde

The H.E.S.S. central data acquisition system

The High Energy Stereoscopic System (H.E.S.S.) is a system of Imaging Atmospheric Cherenkov Telescopes (IACTs) located in the Khomas Highland in Namibia. It measures cosmic gamma rays of very high energies (VHE; >100 GeV) using the Earth's atmosphere as a calorimeter. The H.E.S.S. Array entered Phase II in September 2012 with the inauguration of a fifth telescope that is larger and more complex than the other four. This paper will give an overview of the current H.E.S.S. central data acquisition (DAQ) system with particular emphasis on the upgrades made to integrate the fifth telescope into the array. At first, the various requirements for the central DAQ are discussed then the general design principles employed to fulfil these requirements are described. Finally, the performance, stability and reliability of the H.E.S.S. central DAQ are presented. One of the major accomplishments is that less than 0.8% of observation time has been lost due to central DAQ problems since 2009.Comment: 17 pages, 8 figures, published in Astroparticle Physic

Collisions of particles in locally AdS spacetimes I. Local description and global examples

We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities along a graph $\Gamma$. We impose physically relevant conditions on the cone singularities, e.g. positivity of mass (angle less than $2\pi$ on time-like singular segments). We construct examples of such manifolds, describe the cone singularities that can arise and the way they can interact (the local geometry near the vertices of $\Gamma$). We then adapt to this setting some notions like global hyperbolicity which are natural for Lorentz manifolds, and construct some examples of globally hyperbolic AdS manifolds with interacting particles.Comment: This is a rewritten version of the first part of arxiv:0905.1823. That preprint was too long and contained two types of results, so we sliced it in two. This is the first part. Some sections have been completely rewritten so as to be more readable, at the cost of slightly less general statements. Others parts have been notably improved to increase readabilit

On the total mean curvature of non-rigid surfaces

Using Green's theorem we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field and obtain the following well-known theorem as an immediate consequence: the total mean curvature of a closed smooth surface in the Euclidean 3-space is stationary under an infinitesimal flex.Comment: 4 page

Some open questions on anti-de Sitter geometry

We present a list of open questions on various aspects of AdS geometry, that is, the geometry of Lorentz spaces of constant curvature -1. When possible we point out relations with homogeneous spaces and discrete subgroups of Lie groups, to Teichm\"uller theory, as well as analogs in hyperbolic geometry.Comment: Not a research article in the usual sense but rather a list of open questions. 19 page

Refusing to Endorse. A must Explanation for Pejoratives.

In her analysis of pejoratives, Eva Picardi rejects a too sharp separation between descriptive and expressive content. I reconstruct some of her arguments, endorsing Eva’s criticism of Williamson’s analysis of Dummett and developing a suggestion by Manuel Garcia Carpintero on a speech act analysis of pejoratives. Eva’s main concern is accounting for our instinctive refusal to endorse an assertion containing pejoratives because it suggests a picture of reality we do not share. Her stance might be further developed claiming that uses of pejoratives not only suggest, but also promote a wrong picture of reality. Our refusal to endorse implies rejecting not only a wrong picture of reality but also a call for participation to what that picture promotes

The induced metric on the boundary of the convex hull of a quasicircle in hyperbolic and anti-de Sitter geometry

Celebrated work of Alexandrov and Pogorelov determines exactly which metrics on the sphere are induced on the boundary of a compact convex subset of hyperbolic three-space. As a step toward a generalization for unbounded convex subsets, we consider convex regions of hyperbolic three-space bounded by two properly embedded disks which meet at infinity along a Jordan curve in the ideal boundary. In this setting, it is natural to augment the notion of induced metric on the boundary of the convex set to include a gluing map at infinity which records how the asymptotic geometry of the two surfaces compares near points of the limiting Jordan curve. Restricting further to the case in which the induced metrics on the two bounding surfaces have constant curvature K 2 Π1; 0/ and the Jordan curve at infinity is a quasicircle, the gluing map is naturally a quasisymmetric homeomorphism of the circle. The main result is that for each value of K, every quasisymmetric map is achieved as the gluing map at infinity along some quasicircle. We also prove analogous results in the setting of three-dimensional anti-de Sitter geometry. Our results may be viewed as universal versions of the conjectures of Thurston and Mess about prescribing the induced metric on the boundary of the convex core of quasifuchsian hyperbolic manifolds and globally hyperbolic anti-de Sitter spacetimes