We prove results toward classifying compact Lorentz manifolds on which Heisenberg groups act isometrically. We give a general construction, leading to a new example, of codimension-one actions—those for which the dimension of the Heisenberg group is one less than the dimension of the manifold. The main result is a classification of codimension-one actions, under the assumption they are real-ana...

All the entire solutions to the maximal surface equation in certain 3-dimensional Lorentzian manifolds, obeying the null energy condition, are obtained. Thus, we solve new Calabi–Bernstein problems. As a consequence, the corresponding parametric versions are also given. The behaviour of this Calabi– Bernstein property with respect to an special family of C2-perturbations of Lorentz–Minkowski sp...

We establish Luzin N and Morse–Sard properties for mappings v : Rn → Rm of the Sobolev–Lorentz class Wk p,1 with k = n − m + 1 and p = nk (this is the sharp case that guaranties the continuity of mappings). Using these results we prove that almost all level sets are finite disjoint unions of C1–smooth compact manifolds of dimension n−m.

Einstein's equivalence principle, which states the local equivalence between gravity and acceleration with respect to a frame of reference, requires that a free falling observer result in a co-moving local Minkowski space as a spaceship under only the influence of gravity. However, a "free fall" in a Lorentz manifold may not uniquely result in a local Minkowski space, and a Lorentz manifold wit...

This work is devoted to 2D dispersing billiards with smooth boundary, i.e. periodic Lorentz gases (with and without horizon). We revisit several fundamental properties of these systems and make a number of improvements. The necessity of such improvements became obvious during our recent studies of gases of several particles [CD]. We prove here that local (stable and unstable) manifolds, as well...