Global Conformal Invariants of Submanifolds

The goal of the present paper is to investigate the algebraic structure of global conformal invariants of submanifolds. These are defined to be conformally invariant integrals of geometric scalars of the tangent and normal bundle. A famous example of a global conformal invariant is the Willmore energy of a surface. In codimension one we classify such invariants, showing that under a structural hypothesis (more precisely we assume the integrand depends separately on the intrinsic and extrinsic curvatures, and not on their derivatives) the integrand can only consist of an intrinsic scalar conformal invariant, an extrinsic scalar conformal invariant and the Chern-Gauss-Bonnet integrand. In particular, for codimension one surfaces, we show that the Willmore energy is the unique global conformal invariant, up to the addition of a topological term (the Gauss curvature, giving the Euler Characteristic by the Gauss Bonnet Theorem). A similar statement holds also for codimension two surfaces, once taking into account an additional topological term given by the Chern-Gauss-Bonnet integrand of the normal bundle. We also discuss existence and properties of natural higher dimensional (and codimensional) generalizations of the Willmore energ

Almost Euclidean Isoperimetric Inequalities in Spaces Satisfying Local Ricci Curvature Lower Bounds

Motivated by Perelman's Pseudo Locality Theorem for the Ricci flow, we prove that if a Riemannian manifold has Ricci curvature bounded below in a metric ball which moreover has almost maximal volume, then in a smaller ball (in a quantified sense) it holds an almost-euclidean isoperimetric inequality. The result is actually established in the more general framework of non-smooth spaces satisfying local Ricci curvature lower bounds in a synthetic sense via optimal transportation

Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds

We study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold M. Under the assumption that the sectional curvature of M is strictly positive, we prove the existence of a smoothly immersed sphere minimizing the L^{2} integral of the second fundamental form. Assuming instead that the sectional curvature is less than or equal to 2, and that there exists a point in M with scalar curvature bigger than 6, we obtain a smooth 2-sphere minimizing the integral of 1/4|H|^{2} +1, where H is the mean curvature vector

The Conformal Willmore Functional: a Perturbative Approach

The conformal Willmore functional (which is conformal invariant in general Riemannian manifold $(M,g)$) is studied with a perturbative method: the Lyapunov-Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3, g_\epsilon)$ -where $g_\epsilon$ is a metric close and asymptotic to the euclidean one. With the same technique a non existence result is proved in general Riemannian manifolds $(M,g)$ of dimension three.Comment: 34 pages; Journal of Geometric Analysis, on line first 23 September 201

PRELIMINARY CONCERNS ABOUT AGRONOMIC INTERPRETATION OF NDVI TIME SERIES FROM SENTINEL-2 DATA: PHENOLOGY AND THERMAL EFFICIENCY OF WINTER WHEAT IN PIEMONTE (NW ITALY)

Abstract. TELECER project is supported through Rural Development Programme regional action of EU CAP and is aimed at providing Precision Agriculture–devoted services for cereals monitoring in the Piemonte Region (NW-Italy) context. In this work authors explored some general and preliminary issues mainly aimed at demonstrating and formalizing those evident relationships existing between NDVI image time series and the main ordinary agronomic parameters, with special focus on phenology and thermal efficiency of crops as related to Growing Degrees Day (GDD). Winter wheat was investigated and relationships calibrated at field level, making possible to spatially characterise environmental and management effects. Two different analysis were achieved: (i) one aimed at mapping crop phenological metrics, as derivable from NDVI S2 time series; (ii) one aimed at locally modelling relationship linking GDD and NDVI to somehow test the thermal efficiency of crops in the different parts of the study area. The first analysis showed that the end of season appears to be the most constant phenological metric in the study area possibly demonstrating a time concentration of harvest operations in the area. Differently, the peak of season and the start of season metrics showed to be largely varying in the study, thus suggesting to be stronger predictors: (i) of crop development; (ii) of the effects induced by local agronomical practices. Several base temperatures were used to compute correspondent GDD. These were tested against NDVI and modelled by a parabolic model at field level. Model coefficients distribution were analysed and mapped the correspondent agronomic interpretation suggested

The Tuning System for the HIE-ISOLDE High-Beta Quarter Wave Resonator

A new linac using superconducting quarter-wave resonators (QWR) is under construction at CERN in the framework of the HIE-ISOLDE project. The QWRs are made of niobium sputtered on a bulk copper substrate. The working frequency at 4.5 K is 101.28 MHz and they will provide 6 MV/m accelerating gradient on the beam axis with a total maximum power dissipation of 10 W on cavity walls. A tuning system is required in order to both minimize the forward power variation in beam operation and to compensate the unavoidable uncertainties in the frequency shift during the cool-down process. The tuning system has to fulfil a complex combination of RF, structural and thermal requirements. The paper presents the functional specifications and details the tuning system RF and mechanical design and simulations. The results of the tests performed on a prototype system are discussed and the industrialization strategy is presented in view of final production.Comment: 5 pages, The 16th International Conference on RF Superconductivity (SRF2013), Paris, France, Sep 23-27, 201