On bifurcation of solutions of the Yamabe problem in product manifolds

We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation points of pairwise non-homothetic solutions of the Yamabe problem. Using local rigidity and some compactness results for solutions of the Yamabe problem, we also exhibit new examples of conformal classes (with positive Yamabe constant) for which uniqueness holds. (C) 2011 Elsevier Masson SAS. All rights reserved.

New characterizations for hyperbolic cylinders in anti-de Sitter spaces

In this paper we study complete maximal spacelike hypersurfaces in anti-de Sitter space H-1(n+1) with either constant scalar curvature or constant non-zero Gauss-Kronecker curvature. We characterize the hyperbolic cylinders H-m(c(1)) x Hn-m(c(2)), 1 <= m <= n - 1, as the only such hypersurfaces with (n - 1) principal curvatures with the same sign everywhere. In particular we prove that a complete maximal spacelike hypersurface in H-1(5) with negative constant Gauss-Kronecker curvature is isometric to H-1(c(1)) x H-3(c(2)). (C) 2012 Elsevier Inc. All rights reserved.

A NOTE ON THE UNIQUENESS OF SOLUTIONS FOR THE YAMABE PROBLEM

Using recent results on the compactness of the space of solutions of the Yamabe problem, we show that in conformal classes of metrics near the class of a nondegenerate solution which is unique (up to scaling) the Yamabe problem has a unique solution as well. This provides examples of a local extension, in the space of conformal classes, of a well-known uniqueness criterion due to Obata.

Particle creation due to tachyonic instability in relativistic stars

Dense enough compact objects were recently shown to lead to an exponentially fast increase of the vacuum energy density for some free scalar fields properly coupled to the spacetime curvature as a consequence of a tachyonic-like instability. Once the effect is triggered, the star energy density would be overwhelmed by the vacuum energy density in a few milliseconds. This demands that eventually geometry and field evolve to a new configuration to bring the vacuum back to a stationary regime. Here, we show that the vacuum fluctuations built up during the unstable epoch lead to particle creation in the final stationary state when the tachyonic instability ceases. The amount of created particles depends mostly on the duration of the unstable epoch and final stationary configuration, which are open issues at this point. We emphasize that the particle creation coming from the tachyonic instability will occur even in the adiabatic limit, where the spacetime geometry changes arbitrarily slowly, and therefore is quite distinct from the usual particle creation due to the change in the background geometry.

Shape analysis using fractal dimension: A curvature based approach

The present work shows a novel fractal dimension method for shape analysis. The proposed technique extracts descriptors from a shape by applying a multi-scale approach to the calculus of the fractal dimension. The fractal dimension is estimated by applying the curvature scale-space technique to the original shape. By applying a multi-scale transform to the calculus, we obtain a set of descriptors which is capable of describing the shape under investigation with high precision. We validate the computed descriptors in a classification process. The results demonstrate that the novel technique provides highly reliable descriptors, confirming the efficiency of the proposed method. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4757226]

Scalar field description for parametric models of dark energy

We investigate theoretical and observational aspects of a time-dependent parameterization for the dark energy equation of state w(z), which is a well behaved function of the redshift z over the entire cosmological evolution, i.e., z is an element of [-1, infinity). By using a theoretical algorithm of constructing the quintes-sence potential directly from the w(z) function, we derive and discuss the general features of the resulting potential for the cases in which dark energy is separately conserved and when it is coupled to dark matter. Since the parameterization here discussed allows us to divide the parametric plane in defined regions associated to distinct classes of dark energy models, we use some of the most recent observations from type Ia supernovae, baryon acoustic oscillation peak and Cosmic Microwave Background shift parameter to check which class is observationally preferred. We show that the largest portion of the confidence contours lies into the region corresponding to a possible crossing of the so-called phantom divide line at some point of the cosmic evolution.

EFFECT OF HEAD GROUP AND CURVATURE ON BINDING OF THE ANTIMICROBIAL PEPTIDE TRITRPTICIN TO LIPID MEMBRANES

In this work we examine the interaction between the 13-residue cationic antimicrobial peptide (AMP) tritrpticin (VRRFPWWWPFLRR, TRP3) and model membranes of variable lipid composition. The effect on peptide conformational properties was investigated by means of CD (circular dichroism) and fluorescence spectroscopies. Based on the hypothesis that the antibiotic acts through a mechanism involving toroidal pore formation, and taking into account that models of toroidal pores imply the formation of positive curvature, we used large unilamellar vesicles (LUV) to mimic the initial step of peptide-lipid interaction, when the peptide binds to the bilayer membrane, and micelles to mimic the topology of the pore itself, since these aggregates display positive curvature. In order to more faithfully assess the role of curvature, micelles were prepared with lysophospholipids containing (qualitatively and quantitatively) head groups identical to those of bilayer phospholipids. CD and fluorescence spectra showed that, while TRP3 binds to bilayers only when they carry negatively charged phospholipids. binding to micelles occurs irrespective of surface charge, indicating that electrostatic interactions play a less predominant role in the latter case. Moreover, the conformations acquired by the peptide were independent of lipid composition in both bilayers and micelles. However, the conformations were different in bilayers and in micelles, suggesting that curvature has an influence on the secondary structure acquired by the peptide. Fluorescence data pointed to an interfacial location of TRP3 in both types of aggregates. Nevertheless, experiments with a water soluble fluorescence quencher suggested that the tryptophan residues are more accessible to the quencher in micelles than in bilayers. Thus, we propose that bilayers and micelles can be used as models for the two steps of toroidal pore formation. (C) 2011 Elsevier Ireland Ltd. All rights reserved.