14 research outputs found
Asymptotically hyperbolic manifolds with small mass
For asymptotically hyperbolic manifolds of dimension with scalar
curvature at least equal to the conjectured positive mass theorem
states that the mass is non-negative, and vanishes only if the manifold is
isometric to hyperbolic space. In this paper we study asymptotically hyperbolic
manifolds which are also conformally hyperbolic outside a ball of fixed radius,
and for which the positive mass theorem holds. For such manifolds we show that
the conformal factor tends to one as the mass tends to zero
Constant mean curvature solutions of the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds
We follow the approach employed by Y. Choquet-Bruhat, J. Isenberg and D.
Pollack in the case of closed manifolds and establish existence and
non-existence results for the Einstein-scalar field constraint equations on
asymptotically hyperbolic manifolds.Comment: 15 page
A large class of non constant mean curvature solutions of the Einstein constraint equations on an asymptotically hyperbolic manifold
We construct solutions of the constraint equation with non constant mean
curvature on an asymptotically hyperbolic manifold by the conformal method. Our
approach consists in decreasing a certain exponent appearing in the equations,
constructing solutions of these sub-critical equations and then in letting the
exponent tend to its true value. We prove that the solutions of the
sub-critical equations remain bounded which yields solutions of the constraint
equation unless a certain limit equation admits a non-trivial solution.
Finally, we give conditions which ensure that the limit equation admits no
non-trivial solution.Comment: remark on the equivalence between the existence of a solution to the
Lichnerowicz equation and to the prescribed scalar curvature equation added,
reference [BPB09] added, to appear in Commun. Math. Phy
Conformational and interfacial analyses of K3A18K3 and alamethicin in model membranes.
The involvement of membrane-bound peptides and the influence of protein conformations in several
neurodegenerative diseases lead us to analyze the interactions of model peptides with artificial membranes.
Two model peptides were selected. The first one, an alanine-rich peptide, K3A18K3, was shown to be in
R-helix structures in TFE, a membrane environment-mimicking solvent, while it was mostly -sheeted in
aqueous buffer as revealed by infrared spectroscopy. The other, alamethicin, a natural peptide, was in a stable
R-helix structure. To determine the role of the peptide conformation on the nature of its interactions with
lipids, we compared the structure and topology of the conformational-labile peptide K3A18K3 and of the R-helix
rigid alamethicin in both aqueous and phospholipid environments (Langmuir monolayers and multilamellar
vesicles). K3A18K3 at the air-water interface showed a pressure-dependent orientation of its -sheets, while
the R-helix axis of alamethicin was always parallel to the interface, as probed by polarization modulation
infrared reflection absorption spectroscopy. The -sheeted K3A18K3 peptide was uniformly distributed into
DPPC condensed domains, while the helical-alamethicin insertion distorted the DPPC condensed domains,
as evidenced by Brewster angle microscopy imaging of the air/interface. The -sheeted K3A18K3 interacted
with DMPC multilamellar vesicles via hydrophilic interactions with polar heads and the helical-alamethicin
via hydrophobic interactions with alkyl chains, as shown by infrared spectroscopy and solid state NMR. Our
findings are consistent with the prevailing assumption that the conformation of the peptide predetermines the
mode of interaction with lipids. More precisely, helical peptides tend to be inserted via hydrophobic interactions
within the hydrophobic region of membranes, while -sheeted peptides are predisposed to interact with polar
groups and stay at the surface of lipid laye