Far-field mapping of the longitudinal magnetic and electric optical fields

In this letter, we demonstrate the experimental mapping of the longitudinal magnetic and electric optical fields with a standard scanning microscope that involves a high numerical aperture far-field objective. The imaging concept relies upon the insertion of an azimuthal or a radial polarizer within the detection path of the microscope which acts as an optical electromagnetic filter aimed at transmitting selectively to the detector the signal from the magnetic or electric longitudinal fields present in the detection volume, respectively. The resulting system is thus versatile, non invasive, of high resolution, and shows high detection efficiencies. Magnetic optical properties of physical and biological micro and nano-structures may thus be revealed with a far-field microscope

Eigenvalue pinching and application to the stability and the almost umbilicity of hypersurfaces

In this paper we give pinching theorems for the first nonzero eigenvalue of the Laplacian on the compact hypersurfaces of ambient spaces with bounded sectional curvature. As application we deduce rigidity results for stable constant mean curvature hypersurfaces $M$ of these spaces $N$. Indeed, we prove that if $M$ is included in a ball of radius small enough then the Hausdorff-distance between $M$ and a geodesic sphere $S$ of $N$ is small. Moreover $M$ is diffeomorphic and quasi-isometric to $S$. As other application, we give rigidity results for almost umbilic hypersurfaces

Metric shape of hypersurfaces with small extrinsic radius or large λ1 \lambda_1

We determine the Hausdorff limit-set of the Euclidean hypersurfaces with large $\lambda_1$ or small extrinsic radius. The result depends on the $L^p$ norm of the curvature that is assumed to be bounded a priori, with a critical behaviour for $p$ equal to the dimension minus 1

Why Populist Democracy Promotes Market Liberalization

Using a new set of micro evidence from an original survey of 28 transition countries, we show that democracy increases citizens’ support for the market by guaranteeing income redistribution to inequality-averse agents. Our identification strategy relies on the restriction of the sample to inhabitants of open borders between formerly integrated countries, where people face the same level of market development and economic inequality, as well as the same historically inherited politico-economic culture. Democratic rights increase popular support for the market. This is true, in particular, of inequality-averse agents, provided that they trust political institutions. Our findings suggest that one solution to the recent electoral backlash of reformist parties in the former socialist block lies in a deepening of democracy.democracy, income inequality, redistribution, market liberalization, trust

Democracy, Market Liberalization and Political Preferences

This paper questions the conventional wisdom concerning the sequencing of political and economic reforms in developing countries. We exploit the specific situation of frontier-zones as well as the considerable regional variations in culture and economic development in the countries of Central and Eastern Europe and the former Soviet Union. We estimate the impact of market development and democratization on subjective political preferences. Taking advantage of a new survey conducted in 2006 by the European Bank for Reconstruction and Development and the World Bank in 28 post-transition countries, we find a positive and significant effect of democracy on support for a market economy, but no effect of market liberalization on support for democracy. Our results are robust to the use of various indices of market liberalization and democracy and alternative measures of political preferences.market and democracy ; political preferences ; spatial regression discontinuity ; transition economies