Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.

The Principle of Proportionality in International Law

Whilst the principle of proportionality indisputably plays a crucial role in the protection of fundamental rights, it is still unclear to what extent it applies to other fields in international law. The paper therefore explores the role it plays in selected fields of public international law, beyond human rights. The examination begins in the classical domain of reprisals and in maritime boundary delimitation and continues to analyse the role played in the law of multilateral trade regulation of the World Trade Organization and in bilateral investment protection. In an attempt to explain differences in recourse to proportionality in the various fields, we develop in our conclusions a distinction between horizontal and vertical constellations of legal protection.