Infinitesimal rigidity of a compact hyperbolic 4-orbifold with totally geodesic boundary

Kerckhoff and Storm conjectured that compact hyperbolic n-orbifolds with totally geodesic boundary are infinitesimally rigid when n>3. This paper verifies this conjecture for a specific example based on the 4-dimensional hyperbolic 120-cell.Comment: 9 page

Communication design for health. Territorial and digital networks

In the wake of the Covid-19 pandemic emergency, there has been renewed interest in issues related to health, prevention and community well-being. Health communication and the promotion of disease prevention now require a theoretical and design approach that first and foremost requires the identification of appropriate tools to enhance ‘intersectorality’, ‘collaboration’ and ‘outreach’ among the different areas of expertise of the well-being and healthcare actors involved in the territory. The aim is to strengthen the process of community ‘empowerment’. This study investigates the communicative strategies suitable for enhancing the physical, virtual and digital relationships among the active presences in the territory, choosing those capable of mediating needs, promoting well-being and building a dialogue between citizens and health facilities, thus finally creating a ‘territorial health network’

Constraints for the existence of flat and stable non-supersymmetric vacua in supergravity

We further develop on the study of the conditions for the existence of locally stable non-supersymmetric vacua with vanishing cosmological constant in supergravity models involving only chiral superfields. Starting from the two necessary conditions for flatness and stability derived in a previous paper (which involve the Kahler metric and its Riemann tensor contracted with the supersymmetry breaking auxiliary fields) we show that the implications of these constraints can be worked out exactly not only for factorizable scalar manifolds, but also for symmetric coset manifolds. In both cases, the conditions imply a strong restriction on the Kahler geometry and constrain the vector of auxiliary fields defining the Goldstino direction to lie in a certain cone. We then apply these results to the various homogeneous coset manifolds spanned by the moduli and untwisted matter fields arising in string compactifications, and discuss their implications. Finally, we also discuss what can be said for completely arbitrary scalar manifolds, and derive in this more general case some explicit but weaker restrictions on the Kahler geometry.Comment: 22 pages, Latex, no figure

Two universal results for Wilson loops at strong coupling

We present results for Wilson loops in strongly coupled gauge theories. The loops may be taken around an arbitrarily shaped contour and in any field theory with a dual IIB geometry of the form M x S^5. No assumptions about supersymmetry are made. The first result uses D5 branes to show how the loop in any antisymmetric representation is computed in terms of the loop in the fundamental representation. The second result uses D3 branes to observe that each loop defines a rich sequence of operators associated with minimal surfaces in S^5. The action of these configurations are all computable. Both results have features suggesting a connection with integrability.Comment: 1+12 pages. LaTeX. No figure

Balanced metrics on Cartan and Cartan-Hartogs domains

This paper consists of two results dealing with balanced metrics (in S. Donaldson terminology) on nonconpact complex manifolds. In the first one we describe all balanced metrics on Cartan domains. In the second one we show that the only Cartan-Hartogs domain which admits a balanced metric is the complex hyperbolic space. By combining these results with those obtained in [13] (Kaehler-Einstein submanifolds of the infinite dimensional projective space, to appear in Mathematische Annalen) we also provide the first example of complete, Kaehler-Einstein and projectively induced metric g such that $\alpha g$ is not balanced for all $\alpha >0$.Comment: 11 page

Multi-Hamiltonian structure of Plebanski's second heavenly equation

We show that Plebanski's second heavenly equation, when written as a first-order nonlinear evolutionary system, admits multi-Hamiltonian structure. Therefore by Magri's theorem it is a completely integrable system. Thus it is an example of a completely integrable system in four dimensions

Special biconformal changes of K\"ahler surface metrics

The term "special biconformal change" refers, basically, to the situation where a given nontrivial real-holomorphic vector field on a complex manifold is a gradient relative to two K\"ahler metrics, and, simultaneously, an eigenvector of one of the metrics treated, with the aid of the other, as an endomorphism of the tangent bundle. A special biconformal change is called nontrivial if the two metrics are not each other's constant multiples. For instance, according to a 1995 result of LeBrun, a nontrivial special biconformal change exists for the conformally-Einstein K\"ahler metric on the two-point blow-up of the complex projective plane, recently discovered by Chen, LeBrun and Weber; the real-holomorphic vector field involved is the gradient of its scalar curvature. The present paper establishes the existence of nontrivial special biconformal changes for some canonical metrics on Del Pezzo surfaces, viz. K\"ahler-Einstein metrics (when a nontrivial holomorphic vector field exists), non-Einstein K\"ahler-Ricci solitons, and K\"ahler metrics admitting nonconstant Killing potentials with geodesic gradients.Comment: 16 page

Effect of aggregate type on the fatigue durability of asphalt mixtures

The effect of aggregate type on the fatigue behaviour of asphalt mixtures is an important variable for ensuring greater durability of pavements over time. This study presents the main results of an assessment of the effect of the physical properties of different aggregates on the fatigue behaviour of asphalt mixtures. Two fatigue tests were used for this study, one standardized and another developed recently which evaluates dissipated energy during the cracking of asphalt mixtures (EBADE® test). Three types of aggregates were used and adjusted to a semi-dense aggregate gradation: two of fluvial type (AF1 and AF2) and one from a quarry (AC). Two different shredding processes were used to obtain the aggregates. The results obtained show that there is a strong relationship between the shape and texture of the fine aggregates and the fatigue behaviour of the mixtures. It was also showed that the greater the thickness of the mixture in the pavement structure, the more influence these properties have. Likewise, the shape and texture of the fine aggregate influence the ability of asphalt mixtures to dissipate energy during fatigue damage.Peer ReviewedPostprint (author's final draft

Symplectic geometry on moduli spaces of J-holomorphic curves

Let (M,\omega) be a symplectic manifold, and Sigma a compact Riemann surface. We define a 2-form on the space of immersed symplectic surfaces in M, and show that the form is closed and non-degenerate, up to reparametrizations. Then we give conditions on a compatible almost complex structure J on (M,\omega) that ensure that the restriction of the form to the moduli space of simple immersed J-holomorphic Sigma-curves in a homology class A in H_2(M,\Z) is a symplectic form, and show applications and examples. In particular, we deduce sufficient conditions for the existence of J-holomorphic Sigma-curves in a given homology class for a generic J.Comment: 16 page