Finite energy surfaces and the chord problem
type: Item
instance of: scholarly article
title: Finite energy surfaces and the chord problem
zbMATH Open document ID: 0953.53049
DOI: 10.1215/S0012-7094-99-09608-4
author: Casim Abbas
published in: Duke Mathematical Journal
publication date: 2000-03-27T00:00:00Z
review text: The paper is a study of a conjecture by \textit{V. I. Arnol'd} [Russ. Math. Surv. 41, No. 6, 1-21 (1986; Zbl 0649.58010)] relative to a special class of orbits of the Reeb vector field associated to a contact form. These orbits are called characteristic chords and, as for many important results in symplectic topology, the main tool is \textit{M. Gromov's} theory of pseudoholomorphic curves [Invent. Math. 82, 307-347 (1985; Zbl 0592.53025)], more precisely pseudoholomorphic half-planes of finite energy.
Mathematics Subject Classification ID: 53D10
Mathematics Subject Classification ID: 37J05
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B99
Mathematics Subject Classification ID: 53D35
zbMATH DE Number: 1425181
zbMATH Keywords: contact form
zbMATH Keywords: Reeb vector field
zbMATH Keywords: characteristic chord
zbMATH Keywords: finite energy half-plane
reviewed by: Mircea Crasmareanu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1425181