Comparison theorems for conjugate points in sub-Riemannian geometry

We prove sectional and Ricci-type comparison theorems for the existence of conjugate points along sub-Riemannian geodesics. In order to do that, we regard sub-Riemannian structures as a special kind of variational problems. In this setting, we identify a class of models, namely linear quadratic optimal control systems, that play the role of the constant curvature spaces. As an application, we prove a version of sub-Riemannian Bonnet-Myers theorem and we obtain some new results on conjugate points for three dimensional left-invariant sub-Riemannian structures.Comment: 33 pages, 5 figures, v2: minor revision, v3: minor revision, v4: minor revisions after publicatio

On Jacobi fields and canonical connection in sub-Riemannian geometry

In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like invariants. We show that these coefficients can be interpreted as the curvature of a canonical Ehresmann connection associated to the metric, first introduced in [Zelenko-Li]. We show why this connection is naturally nonlinear, and we discuss some of its properties.Comment: 13 pages, (v2) minor corrections. Final version to appear on Archivum Mathematicu

Sand transverse dune aerodynamics: 3D Coherent Flow Structures from a computational study

The engineering interest about dune fields is dictated by the their interaction with a number of human infrastructures in arid environments. Sand dunes dynamics is dictated by wind and its ability to induce sand erosion, transport and deposition. A deep understanding of dune aerodynamics serves then to ground effective strategies for the protection of human infrastructures from sand, the so-called sand mitigation. Because of their simple geometry and their frequent occurrence in desert area, transverse sand dunes are usually adopted in literature as a benchmark to investigate dune aerodynamics by means of both computational or experimental approaches, usually in nominally 2D setups. The present study aims at evaluating 3D flow features in the wake of a idealised transverse dune, if any, under different nominally 2D setup conditions by means of computational simulations and to compare the obtained results with experimental measurements available in literature

The Non-Linear Cournot Model as a Best-Response Potential Game

potential function, potential game, Cournot oligopoly

Thinness and Obesity: A Model of Food Consumption, Health Concerns, and Social Pressure

The increasing concern of the policy maker about eating behavior has focused on thespread of obesity and on the evidence of a consistent number of individuals dietingdespite being underweight. As the latter behavior is often attributed to the socialpressure to be thin, some governments have already taken actions to ban ultra-thinideals and testimonials. Assuming that people are heterogeneous in their healthyweights, but are exposed to the same ideal body weight, this paper proposes atheoretical framework to assess whether increasing the ideal body weight is sociallydesirable, both from a welfare and from a health point of view. If being overweightis the average condition and the ideal body weight is thin, increasing the ideal bodyweight may increase welfare by reducing social pressure. By contrast, health is onaverage reduced, since people depart even further from their healthy weight. Giventhat in the US and in Europe people are on average overweight, we conclude thatthese policies, even when are welfare improving, may foster the obesity epidemic.Body Weight, Diet, Obesity, Social Pressure, Underweight.

Invariant measures for systems of Kolmogorov equations

In this paper we provide sufficient conditions which guarantee the existence of a system of invariant measures for semigroups associated to systems of parabolic differential equations with unbounded coefficients. We prove that these measures are absolutely continuous with respect to the Lebesgue measure and study some of their main properties. Finally, we show that they characterize the asymptotic behaviour of the semigroup at infinity