On the Gauss map of embedded minimal tubes

A surface is called a tube if its level-sets with respect to some coordinate function (the axis of the surface) are compact. Any tube of zero mean curvature has an invariant, the so-called flow vector. We study how the geometry of the Gaussian image of a higher-dimensional minimal tube M is controlled by the angle alpha(M) between the axis and the flow vector of M. We prove that the diameter of the Gauss image of M is at least 2alpha(M). As a consequence we derive an estimate on the length of a two-dimensional minimal tube M in terms of alpha(\M) and the total Gaussian curvature of M

Production of Massive Fermions at Preheating and Leptogenesis

We present a complete computation of the inflaton decay into very massive fermions during preheating. We show that heavy fermions are produced very efficiently up to masses of order 10^{17}-10^{18} GeV; the accessible mass range is thus even broader than the one for heavy bosons. We apply our findings to the leptogenesis scenario, proposing a new version of it, in which the massive right-handed neutrinos, responsible for the generation of the baryon asymmetry, are produced during preheating. We also discuss other production mechanisms of right-handed neutrinos in the early Universe, identifying the neutrino mass parameters for which the observed baryon asymmetry is reproduced.Comment: 29 pages, 4 figure

Features of translating technical terms in Portuguese and English

The article deals with the main difficulties and features of militar

Denjoy-Ahlfors Theorem for Harmonic Functions on Riemannian Manifolds and External Structure of Minimal Surfaces

We extend the well-known Denjoy-Ahlfors theorem on the number of different asymptotic tracts of holomorphic functions to subharmonic functions on arbitrary Riemannian manifolds. We obtain some new versions of the Liouville theorem for \p-harmonic functions without requiring the geodesic completeness requirement of a manifold. Moreover, an upper estimate of the topological index of the height function on a minimal surface in $\R{n}$ has been established and, as a consequence, a new proof of Bernstein's theorem on entire solutions has been derived. Other applications to minimal surfaces are also discussed.Comment: 30 page

Quantum Dew

We consider phase separation in nonequilibrium Bose gas with an attractive interaction between the particles. Using numerical integrations on a lattice, we show that the system evolves into a state that contains drops of Bose-Einstein condensate suspended in uncondensed gas. When the initial gas is sufficiently rarefied, the rate of formation of this quantum dew scales with the initial density as expected for a process governed by two-particle collisions.Comment: 4 pages, revtex, 5 figure