176 research outputs found
Conformal dimension and random groups
We give a lower and an upper bound for the conformal dimension of the
boundaries of certain small cancellation groups. We apply these bounds to the
few relator and density models for random groups. This gives generic bounds of
the following form, where is the relator length, going to infinity.
(a) 1 + 1/C < \Cdim(\bdry G) < C l / \log(l), for the few relator model,
and
(b) 1 + l / (C\log(l)) < \Cdim(\bdry G) < C l, for the density model, at
densities .
In particular, for the density model at densities , as the relator
length goes to infinity, the random groups will pass through infinitely
many different quasi-isometry classes.Comment: 32 pages, 4 figures. v2: Final version. Main result improved to
density < 1/16. Many minor improvements. To appear in GAF
A Combination Theorem for Metric Bundles
We define metric bundles/metric graph bundles which provide a purely
topological/coarse-geometric generalization of the notion of trees of metric
spaces a la Bestvina-Feighn in the special case that the inclusions of the edge
spaces into the vertex spaces are uniform coarsely surjective quasi-isometries.
We prove the existence of quasi-isometric sections in this generality. Then we
prove a combination theorem for metric (graph) bundles (including exact
sequences of groups) that establishes sufficient conditions, particularly
flaring, under which the metric bundles are hyperbolic. We use this to give
examples of surface bundles over hyperbolic disks, whose universal cover is
Gromov-hyperbolic. We also show that in typical situations, flaring is also a
necessary condition.Comment: v3: Major revision: 56 pages 5 figures. Many details added.
Characterization of convex cocompact subgroups of mapping class groups of
surfaces with punctures in terms of relative hyperbolicity given v4: Final
version incorporating referee comments: 63 pages 5 figures. To appear in
Geom. Funct. Ana
Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential
The S-wave effective range parameters of the neutron-deuteron (nd) scattering
are derived in the Faddeev formalism, using a nonlocal Gaussian potential based
on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy
eigenphase shift is sufficiently attractive to reproduce predictions by the
AV18 plus Urbana three-nucleon force, yielding the observed value of the
doublet scattering length and the correct differential cross sections below the
deuteron breakup threshold. This conclusion is consistent with the previous
result for the triton binding energy, which is nearly reproduced by fss2
without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy
Non-Canonical NF-κB Activation and Abnormal B Cell Accumulation in Mice Expressing Ubiquitin Protein Ligase-Inactive c-IAP2
Loss of c-IAP2 ubiquitin ligase activity, which occurs in the lymphoma-causing c-IAP2/MALT1 fusion protein, activates non-canonical NF-κB signaling and results in B cell abnormalities characteristic of MALT lymphoma
Anosov representations: Domains of discontinuity and applications
The notion of Anosov representations has been introduced by Labourie in his
study of the Hitchin component for SL(n,R). Subsequently, Anosov
representations have been studied mainly for surface groups, in particular in
the context of higher Teichmueller spaces, and for lattices in SO(1,n). In this
article we extend the notion of Anosov representations to representations of
arbitrary word hyperbolic groups and start the systematic study of their
geometric properties. In particular, given an Anosov representation of
into G we explicitly construct open subsets of compact G-spaces, on which
acts properly discontinuously and with compact quotient.
As a consequence we show that higher Teichmueller spaces parametrize locally
homogeneous geometric structures on compact manifolds. We also obtain
applications regarding (non-standard) compact Clifford-Klein forms and
compactifications of locally symmetric spaces of infinite volume.Comment: 63 pages, accepted for publication in Inventiones Mathematica
Regulation of the small regulatory RNA MicA by ribonuclease III: a target-dependent pathway
MicA is a trans-encoded small non-coding RNA, which downregulates porin-expression in stationary-phase. In this work, we focus on the role of endoribonucleases III and E on Salmonella typhimurium sRNA MicA regulation. RNase III is shown to regulate MicA in a target-coupled way, while RNase E is responsible for the control of free MicA levels in the cell. We purified both Salmonella enzymes and demonstrated that in vitro RNase III is only active over MicA when in complex with its targets (whether ompA or lamB mRNAs). In vivo, MicA is demonstrated to be cleaved by RNase III in a coupled way with ompA mRNA. On the other hand, RNase E is able to cleave unpaired MicA and does not show a marked dependence on its 5′ phosphorylation state. The main conclusion of this work is the existence of two independent pathways for MicA turnover. Each pathway involves a distinct endoribonuclease, having a different role in the context of the fine-tuned regulation of porin levels. Cleavage of MicA by RNase III in a target-dependent fashion, with the concomitant decay of the mRNA target, strongly resembles the eukaryotic RNAi system, where RNase III-like enzymes play a pivotal role
Definitions of quasiconformality
We establish that the infinitesimal “ H -definition” for quasiconformal mappings on Carnot groups implies global quasisymmetry, and hence the absolute continuity on almost all lines. Our method is new even in R n where we obtain that the “limsup” condition in the H -definition can be replaced by a “liminf” condition. This leads to a new removability result for (quasi)conformal mappings in Euclidean spaces. An application to parametrizations of chord-arc surfaces is also given.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46582/1/222_2005_Article_BF01241122.pd
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