The Weinstein Conjecture for Planar Contact Structures in Dimension\n Three

2004/09/20 by Casim Abbas, Abbas, Casim, Kai Cieliebak +3 · 1 citation
Engineering · Mathematics · #53D35 #57R57 #70H12 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.math/0409355

openalex publication_date 2004/09/20 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28

Abstract

In this paper we describe a general strategy for approaching the Weinstein\nconjecture in dimension three. We apply this approach to prove the Weinstein\nconjecture for a new class of contact manifolds (planar contact manifolds). We\nalso discuss how the present approach reduces the general Weinstein conjecture\nin dimension three to a compactness problem for the solution set of a first\norder elliptic PDE.\n

Citations

• Fredholm theory and transversality for noncompact pseudoholomorphic mapsin symplectizations

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