The Weinstein Conjecture for Planar Contact Structures in Dimension Three

Details The Weinstein Conjecture for Planar Contact Structures in Dimension Three The Weinstein Conjecture for Planar Contact Structures in Dimension Three

2004-09-20

arxiv.org/abs/math/0409355v2

Mathematics

Symplectic Geometry

19 pages, corrected some typos

Scientific paper

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.

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