CR structures on real hypersurfaces of a complex projective space.
The aim of this paper is to investigate n-dimensional real submanifolds of complex manifolds in the case when the maximal holomorphic tangent space is (n-1)-dimensional. In particular, we give some examples and we consider the Levi form on these submanifolds, especially when the ambient space is a complex space form. Moreover, we show that on some remarkable class of real hypersurfaces of complex space forms, the Levi form cannot vanish identically.
A mini-introduction to critical phenomena in gravitational collapse is combined with a more detailed discussion of how gravity regularizes the 'critical spacetimes' that dominate these phenomena.
We study two classes of linear representations of a surface group: Hitchin and maximal symplectic representations. We relate them to cross ratios and thus deduce that they are displacing which means that their translation lengths are roughly controlled by the translations lengths on the Cayley graph. As a consequence, we show that the mapping class group acts properly on the space of representations and that the energy functional associated to such a representation is proper. This implies the existence...