14 citations · 44 across the 6 of their papers we have counts for
6 papers
Holomorphic Open Book Decompositions
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 th…
The Weinstein Conjecture for Planar Contact Structures in Dimension Three
Casim Abbas, Kai Cieliebak, Helmut Hofer
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 o…
Pseudoholomorphic strips in symplectisations III: Embeding properties and compactness
Casim Abbas
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 bou…
Pseudoholomorphic Strips in Symplectisations II: Fredholm theory and Transversality
Casim Abbas
See http://www.math.msu.edu/~abbas or Wiley preprint server.
Pseudoholomorphic Strips in Symplectisations I: Asymptotic Behavior
Casim Abbas
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 symplect…
The Chord Problem and a new method of filling by pseudoholomorphic curves
Casim Abbas
In this paper we give a simple application of the filling methods developed earlier to the chord problem in three dimensional contact geometry.