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.
Cite this article
Casim Abbas, Kai Cieliebak, Helmut W. Hofer, The Weinstein conjecture for planar contact structures in dimension three. Comment. Math. Helv. 80 (2005), no. 4, pp. 771–793DOI 10.4171/CMH/34