Commentarii Mathematici Helvetici


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Volume 80, Issue 4, 2005, pp. 771–793
DOI: 10.4171/CMH/34

Published online: 2005-12-31

The Weinstein conjecture for planar contact structures in dimension three

Casim Abbas[1], Kai Cieliebak[2] and Helmut W. Hofer[3]

(1) Michigan State University, East Lansing, USA
(2) Universit├Ąt Augsburg, Germany
(3) Institute for Advanced Study, Princeton, USA

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.

Keywords: Contact structure, open book, periodic orbit, holomorphic curve

Abbas Casim, Cieliebak Kai, Hofer Helmut: The Weinstein conjecture for planar contact structures in dimension three. Comment. Math. Helv. 80 (2005), 771-793. doi: 10.4171/CMH/34