We extend the validity of Dain’s angular-momentum inequality to maximal, asymptotically flat, initial data sets on a simply connected manifold with several asymptotically flat ends which are invariant under a U(1) action and which admit a twist potential.

We give a topological interpretation of the space of L2-harmonic forms on Manifold with flat ends. It is an answer to an old question of J. Dodziuk. We also give a Chern-Gauss-Bonnet formula for the L2-Euler characteristic of some of these Manifolds. These results are applications of general theorems on complete Riemannian Manifold whose Gauss-Bonnet operator is nonparabolic at infinity. Résumé...

In this paper we give a conformal representation of flat surfaces in the hyperbolic 3space using the complex structure induced by its second fundamental form. We also study some examples and the behaviour at infinity of complete flat ends. Mathematics Subject Classification (1991): 53A35, 53C42

Negative stiffness is understood as the occurrence of a force in the same direction as the imposed deformation. Structures and composites with negative stiffness elements enable a large amplification in damping. It is shown in this work, using an experimental approach, that when a flexible flat-ends column is aligned in a post-buckled condition, a negative structural stiffness and large hystere...