A Morse Theory for Massive Particles and Photons in General Relativity

In this paper we develop a Morse Theory for timelike geodesics parameterized by a constant multiple of proper time. The results are obtained using an extension to the timelike case of the relativistic Fermat Principle, and techniques from Global Analysis on infinite dimensional manifolds. In the second part of the paper we discuss a limit process that allows to obtain also a Morse theory for light rays

Geodesic connectedness and conjugate points in GRW spacetimes

Given two points of a Generalized Robertson-Walker spacetime, the existence, multiplicity and causal character of geodesic connecting them is characterized. Conjugate points of such geodesics are related to conjugate points of geodesics on the fiber, and Morse-type relations are obtained. Applications to bidimensional spacetimes and to GRW spacetimes satisfying the timelike convergence condition are also found.Comment: 31 pages and 2 figure

Existence of orthogonal geodesic chords on Riemannian manifolds with concave boundary and homeomorphic to the N-dimensional disk

In this paper we give a proof of the existence of an orthogonal geodesic chord on a Riemannian manifold homeomorphic to a closed disk and with concave boundary. This kind of study is motivated by the link of the multiplicity problem with the famous Seifert conjecture (formulated in 1948) about multiple brake orbits for a class of Hamiltonian systems at a fixed energy level.Comment: 59 pages, 3 figures. To appear on Nonlinear Analysis Series A: Theory, Methods & Application

On the normal exponential map in singular conformal metrics

Brake orbits and homoclinics of autonomous dynamical systems correspond, via Maupertuis principle, to geodesics in Riemannian manifolds endowed with a metric which is singular on the boundary (Jacobi metric). Motivated by the classical, yet still intriguing in many aspects, problem of establishing multiplicity results for brake orbits and homoclinics, as done in [6, 7, 10], and by the development of a Morse theory in [8] for geodesics in such kind of metric, in this paper we study the related normal exponential map from a global perspective.Comment: 10 page

Assessing changes in the monetary transmission mechanism: a VAR approach

Paper for a conference sponsored by the Federal Reserve Bank of New York entitled Financial Innovation and Monetary TransmissionEconomic conditions - United States ; Monetary policy

Determinants of Health Disparities in Italian Regions

There is an extensive literature on regional disparities in health, but much of thisliterature focuses on the United States. Among European countries, Italy is the country whereregional health disparities contribute the most to socioeconomic health disparities. In this paper,we report on regional differences in self-reported poor health and explore possible determinantsat the individual and regional levels in Italy. We use data from the “Indagine Multiscopo sulle Famiglie”, a survey of aspects ofeveryday life in the Italian population, to estimate multilevel logistic regressions that model poorself-reported health as a function of individual and regional socioeconomic factors. Next we usethe causal step approach to test if living conditions, healthcare characteristics, social isolation,2and health behaviors at the regional level mediate the relationship between regionalsocioeconomic factors and self-rated health. We find that residents living in regions with more poverty, more unemployment, andmore income inequality are more likely to report poor health and that poor living conditions andprivate share of healthcare expenditures at the regional level are determinants of socioeconomicdisparities in self-rated health among Italian regions. The implications are that regional contexts matter and that regional policies in Italyhave the potential to reduce health disparities by implementing interventions aimed at improvingliving conditions and access to quality healthcare.health inequality, Italy, self-reported health, regional health disparities

Morse Theory for geodesics in singular conformal metrics

Motivated by the use of degenerate Jacobi metrics for the study of brake orbits and homoclinics, we develop a Morse theory for geodesics in conformal metrics having conformal factors vanishing on a regular hypersurface of a Riemannian manifold.Comment: 22 pages. To appear in Communications in Analysis and Geometr