The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations

In this paper we deal with some problems concerning minimal hypersurfaces in Carnot-Caratheodory (CC) structures. More precisely we will introduce a general calibration method in this setting and we will study the Bernstein problem for entire regular intrinsic minimal graphs in a meaningful and simpler class of CC spaces, i.e. the Heisenberg group H^n. In particular we will positively answer to the Bernstein problem in the case n=1 and we will provide counterexamples when n>=5

Lorentzian compact manifolds: isometries and geodesics

In this work we investigate families of compact Lorentzian manifolds in dimension four. We show that every lightlike geodesic on such spaces is periodic, while there are closed and non-closed spacelike and timelike geodesics. Their isometry groups are computed. We also show that there is a non trivial action by isometries of \Heis_3(\RR) on the nilmanifold S^1\times (\Gamma_k \bsh \Heis_3(\RR)) for $\Gamma_k$ a lattice of \Heis_3(\RR).Comment: 17 page

A dynamical approach to the Sard problem in Carnot groups

We introduce a dynamical-systems approach for the study of the Sard problem in sub-Riemannian Carnot groups. We show that singular curves can be obtained by concatenating trajectories of suitable dynamical systems. As an application, we positively answer the Sard problem in some classes of Carnot groups

Kelvin probe characterization of buried graphitic microchannels in single-crystal diamond

In this work, we present an investigation by Kelvin Probe Microscopy (KPM) of buried graphitic microchannels fabricated in single-crystal diamond by direct MeV ion microbeam writing. Metal deposition of variable-thickness masks was adopted to implant channels with emerging endpoints and high temperature annealing was performed in order to induce the graphitization of the highly-damaged buried region. When an electrical current was flowing through the biased buried channel, the structure was clearly evidenced by KPM maps of the electrical potential of the surface region overlying the channel at increasing distances from the grounded electrode. The KPM profiling shows regions of opposite contrast located at different distances from the endpoints of the channel. This effect is attributed to the different electrical conduction properties of the surface and of the buried graphitic layer. The model adopted to interpret these KPM maps and profiles proved to be suitable for the electronic characterization of buried conductive channels, providing a non-invasive method to measure the local resistivity with a micrometer resolution. The results demonstrate the potential of the technique as a powerful diagnostic tool to monitor the functionality of all-carbon graphite/diamond devices to be fabricated by MeV ion beam lithography.Comment: 21 pages, 5 figure

HOMOGENEOUS RIEMANNIAN MANIFOLDS WITH NON-TRIVIAL NULLITY

We develop a general theory for irreducible homogeneous spaces M = G/H, in relation to the nullity distribution ν of their curvature tensor. We construct natural invariant (different and increasing) distributions associated with the nullity, that give a deep insight of such spaces. In particular, there must exist an order-two transvection, not in the nullity, with null Jacobi operator. This fact was very important for finding out the first homogeneous examples with non-trivial nullity, i.e., where the nullity distribution is not parallel. Moreover, we construct irreducible examples of conullity k = 3, the smallest possible, in any dimension. None of our examples admit a quotient of finite volume. We also proved that H is trivial and G is solvable if k = 3. Another of our main results is that the leaves, i.e., the integral manifolds, of the nullity are closed (we used a rather delicate argument). This implies that M is a Euclidean affine bundle over the quotient by the leaves of ν. Moreover, we prove that ν⊥ defines a metric connection on this bundle with transitive holonomy or, equivalently, ν⊥ is completely non-integrable (this is not in general true for an arbitrary autoparallel and at invariant distribution). We also found some general obstruction for the existence of non-trivial nullity: e.g., if G is reductive (in particular, if M is compact), or if G is two-step nilpotent

Average energy dissipated by mega-electron-volt hydrogen and helium ions per electron-hole pair generation in 4H-SiC

The pulse height response for He and H ions with energies between 1 and 6 MeV incident upon n-type 4H-SiC epitaxial Schottky diodes has been investigated. The average amount of energy, ε, given up by the incident radiation to form electron-hole pair in this material was obtained by comparison with the average energy loss per pair in silicon detectors and it was found to be (7.78±0.05)eV at room temperature. This value is smaller than that foreseen by Klein's semiempirical linear relationship between ε and the semiconductor band gap

Photocurrent study of beta-ray priming in CVD diamond

Priming by X-rays or by beta-rays is generally needed in order to qualify CVD diamond for nuclear detection or for dosimetry. The priming effect is usually attributed in filling the hole traps, which are responsible for the charge collection efficiency of the detector. Emptying the filled traps can be easily detected by Thermoluminescence (TL), which is considered to be a measure of the absorbed dose. In this work, we prove that below-gap photocurrent (BGPC) can also be used in the same way and it is dominated by the optical detrapping of holes from the same centers. Time dependence of this beta-rays induced persistent photocurrent (PPC), which in fact, depends only on the total number of photons impinging onto the sample. In fact, at long times or for large number of photons, the photocurrent approaches to the same limit of PC for a null dose. The hole trapping centers distribution seems to extend from 1.25 to 2.5 eV valence band

Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions of a balance equation

In this paper we provide a characterization of intrinsic Lipschitz graphs in the sub-Riemannian Heisenberg groups in terms of their distributional gradients. Moreover, we prove the equivalence of different notions of continuous weak solutions to the equation \phi_y+ [\phi^{2}/2]_t=w, where w is a bounded function depending on \phi