Finite-energy pseudoholomorphic planes with multiple asymptotic limits
| Autor: | Richard Siefring |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
General Mathematics 010102 general mathematics Degenerate energy levels Pseudoholomorphic curve Torus Homology (mathematics) Lambda 01 natural sciences Exponential function Mathematics - Symplectic Geometry 32Q65 53D42 0103 physical sciences Reeb vector field FOS: Mathematics Symplectic Geometry (math.SG) 010307 mathematical physics 0101 mathematics Mathematics::Symplectic Geometry Mathematics Symplectic geometry |
| Popis: | It's known from from work of Hofer, Wysocki, and Zehnder [1996] and Bourgeois [2002] that in a contact manifold equipped with either a nondegenerate or Morse-Bott contact form, a finite-energy pseudoholomorphic curve will be asymptotic at each of its non removable punctures to a single periodic orbit of the Reeb vector field and that the convergence is exponential. We provide examples here to show that this need not be the case if the contact form is degenerate. More specifically, we show that on any contact manifold $(M, \xi)$ with cooriented contact structure one can choose a contact form $\lambda$ with $\ker\lambda=\xi$ and a compatible complex structure $J$ on $\xi$ so that for the associated $\mathbb{R}$-invariant almost complex structure $\tilde J$ on $\mathbb{R}\times M$ there exist families of embedded finite-energy $\tilde J$-holomorphic cylinders and planes having embedded tori as limit sets. Comment: 16 pages; some typos fixed and minor edits made; to appear in Mathematische Annalen |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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