Quasiconvexity and relatively hyperbolic groups that split

We explore the combination theorem for a group G splitting as a graph of relatively hyperbolic groups. Using the fine graph approach to relative hyperbolicity, we find short proofs of the relative hyperbolicity of G under certain conditions. We then provide a criterion for the relative quasiconvexity of a subgroup H depending on the relative quasiconvexity of the intersection of H with the vertex groups of G. We give an application towards local relative quasiconvexity

Rank-(n – 1) convexity and quasiconvexity for divergence free fields

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Rank-(n – 1) convexity and quasiconvexity for divergence free fields

The CAST experiment at CERN (European Organization of Nuclear Research) searches for axions from the sun. The axion is a pseudoscalar particle that was motivated by theory thirty years ago, with the intention to solve the strong CP problem. Together with the neutralino, the axion is one of the most promising dark matter candidates. The CAST experiment has been taking data during the last two years, setting an upper limit on the coupling of axions to photons more restrictive than from any other solar axion search in the mass range below 0.1 eV. In 2005 CAST will enter a new experimental phase extending the sensitivity of the experiment to higher axion masses. The CAST experiment strongly profits from technology developed for high energy physics and for X-ray astronomy: A superconducting prototype LHC magnet is used to convert potential axions to detectable X-rays in the 1-10 keV range via the inverse Primakoff effect. The most sensitive detector system of CAST is a spin-off from space technology, a Wolter I type X-ray optics in combination with a prototype pn-CCD developed for ESA's XMM-Newton mission. As in other rare event searches, background suppression and a thorough shielding concept is essential to improve the sensitivity of the experiment to the best possible. In this context CAST offers the opportunity to study the background of pn-CCDs and its long term behavior in a terrestrial environment with possible implications for future space applications. We will present a systematic study of the detector background of the pn-CCD of CAST based on the data acquired since 2002 including preliminary results of our background simulations.Comment: 11 pages, 8 figures, to appear in Proc. SPIE 5898, UV, X-Ray, and Gamma-Ray Space Instrumentation for Astronomy XI

Potentials for A\mathcal{A}-quasiconvexity

We show that each constant rank operator $\mathcal{A}$ admits an exact potential $\mathbb{B}$ in frequency space. We use this fact to show that the notion of $\mathcal{A}$-quasiconvexity can be tested against compactly supported fields. We also show that $\mathcal{A}$-free Young measures are generated by sequences $\mathbb{B}u_j$, modulo shifts by the barycentre.Comment: 15 pages; to appear in Calculus of Variations and Partial Differential Equation

Separation of Relatively Quasiconvex Subgroups

Suppose that all hyperbolic groups are residually finite. The following statements follow: In relatively hyperbolic groups with peripheral structures consisting of finitely generated nilpotent subgroups, quasiconvex subgroups are separable; Geometrically finite subgroups of non-uniform lattices in rank one symmetric spaces are separable; Kleinian groups are subgroup separable. We also show that LERF for finite volume hyperbolic 3-manifolds would follow from LERF for closed hyperbolic 3-manifolds. The method is to reduce, via combination and filling theorems, the separability of a quasiconvex subgroup of a relatively hyperbolic group G to the separability of a quasiconvex subgroup of a hyperbolic quotient G/N. A result of Agol, Groves, and Manning is then applied.Comment: 22 pages, 2 figures. New version has numbering matching with the published version in the Pacific Journal of Mathematics, 244 no. 2 (2010) 309--334