ar X iv : 0 70 7 . 19 46 v 1 [ m at h . D G ] 1 3 Ju l 2 00 7 The uniqueness of the helicoid in the Lorentz - Minkowski space

ar X iv : 0 70 7 . 40 46 v 1 [ m at h . A G ] 2 7 Ju l 2 00 7 CLIFFORD ’ S THEOREM FOR COHERENT SYSTEMS

Let C be an algebraic curve of genus g ≥ 2. We prove an analogue of Clifford’s theorem for coherent systems on C and some refinements using results of Re and Mercat.

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

We prove an existence and uniqueness result for ground states of one-dimensional Schrödinger-Newton equations.

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 : 0 70 7 . 19 72 v 1 [ gr - q c ] 1 3 Ju l 2 00 7 Boost Invariant Marginally Trapped Surfaces in Minkowski 4 - Space

The extremal and partly marginally trapped surfaces in Minkowski 4-space, which are invariant under the group of boost isometries, are classified. Moreover, it is shown that there do not exist extremal surfaces of this kind with constant Gaussian curvature. A procedure is given in order to construct a partly marginally trapped surface by gluing two marginally trapped surfaces which are invarian...

ar X iv : 0 70 7 . 42 19 v 1 [ m at h . D G ] 2 8 Ju l 2 00 7 Real embeddings , η - invariant and Chern - Simons current ∗

We present an alternate proof of the Bismut-Zhang localization formula for η-invariants without using the analytic techniques developed by Bismut-Lebeau. A Riemann-Roch property for Chern-Simons currents, which is of independent interest, is established in due course.