ar X iv : 0 70 7 . 03 46 v 1 [ m at h - ph ] 3 J ul 2 00 7 THE ONE - DIMENSIONAL SCHRÖDINGER - NEWTON EQUATIONS

ar X iv : 0 71 2 . 31 03 v 1 [ m at h - ph ] 1 9 D ec 2 00 7 STATIONARY SOLUTIONS OF THE SCHRÖDINGER - NEWTON MODEL - AN ODE APPROACH

We prove the existence and uniqueness of stationary spherically symmetric positive solutions for the Schrödinger-Newton model in any space dimension d. Our result is based on a careful analysis of the corresponding system of second order differential equations. It turns out that d = 6 is critical for the existence of finite energy solutions and the equations for positive spherically symmetric s...

ar X iv : 0 70 7 . 33 03 v 1 [ m at h . O A ] 2 3 Ju l 2 00 7 OPERATOR - VALUED FRAMES

ar X iv : m at h - ph / 0 30 70 15 v 1 8 J ul 2 00 3 Integrable geodesic flows on Riemannian manifolds : Construction and Obstructions ∗ Alexey

This paper is a review of recent and classical results on integrable geodesic flows on Riemannian manifolds and topological obstructions to integrability. We also discuss some open problems.

ar X iv : 0 70 7 . 04 47 v 1 [ m at h . R A ] 3 J ul 2 00 7 Subrings which are closed with respect to taking the inverse

Let S be a subring of the ring R. We investigate the question of whether S ∩ U(R) = U(S) holds for the units. In many situations our answer is positive. There is a special emphasis on the case when R is a full matrix ring and S is a structural subring of R defined by a reflexive and transitive relation.

ar X iv : 0 70 7 . 03 76 v 1 [ m at h . FA ] 3 J ul 2 00 7 SELF IMPROVING SOBOLEV - POINCARÉ INEQUALITIES , TRUNCATION AND SYMMETRIZATION

In our recent paper [12] we developed a new principle of “symmetrization by truncation” to obtain symmetrization inequalities of Sobolev type via truncation. In this note we consider the corresponding results for Sobolev spaces on domains, without assuming that the Sobolev functions vanish at the boundary. The explicit connection between Sobolev-Poincaré inequalities and isoperimetric inequalit...