arXiv subjects
Publications and source records attributed to Casim Abbas.
Emmanuel Giroux showed that every contact structure on a closed three dimensional manifold is supported by an open book decomposition. We will extend this result by showing that the open book decomposition can be chosen in such a way that the pages are solutions to a homologically perturbed Holomorphic Curve equation.
In this paper we describe a general strategy for approaching the Weinstein conjecture in dimension three. We apply this approach to prove the Weinstein conjecture for a new class of contact manifolds (planar contact manifolds). We also discuss how the present approach reduces the general Weinstein conjecture in dimension three to a compactness problem for the solution set of a first order elliptic PDE.
In this paper we give a simple application of the filling methods developed earlier to the chord problem in three dimensional contact geometry.
This paper is the last in a series of three papers which investigate pseudoholomorphic strips in the symplectisation of a three dimensional closed contact manifold with a mixed boundary condition. We will prove a compactness and an intersection result, and we will investigate the embedding properties of such pseudoholomorphic curves.
See http://www.math.msu.edu/~abbas or Wiley preprint server.
This paper is part of a larger program, the investigation of the Chord Problem in three dimensional contact geometry. The main tool will be pseudoholomorphic strips in the symplectisation of a three dimensional contact manifold with two totally real submanifolds $L_0,L_1$ as boundary conditions. The submanifolds $L_0$ and $L_1$ do not intersect transversally. The subject of this paper is to study the asymptotic behavior of such pseudoholomorphic strips.