Abstract
AbstractThis is a review article on pseudo-holomorphic curves which attempts at touching all the main analytical results. The goal is to make a user friendly introduction which is accessible to those without an analytical background. Indeed, the major accomplishment of this review is probably its short length.Nothing in here is original and can be found in more detailed accounts such as [6] and [8]. The exposition of the compactness theorem is somewhat different from that in the standard references and parts of it are imported from harmonic map theory [7], [5]. The references used are listed, but of course any mistake is my own fault.
Highlights
This is a review article on pseudo-holomorphic curves which attempts at touching all the main analytical results
The exposition of the compactness theorem is somewhat di erent from that in the standard references and parts of it are imported from harmonic map theory [7], [5]
Let u : Σ → M be a pseudo-holomorphic curve and e : Σ → R the associated energy density de ned by e = |du| , see remark 2
Summary
This is a review article on pseudo-holomorphic curves which attempts at touching all the main analytical results. The following result shows that pseudo-holomorphic maps minimize the harmonic map energy amongst maps with homologous image. Let (M, ω, J) be a symplectic manifold equipped with a compatible almost complex structure and u : Σ → M a pseudo-holomorphic curve1.
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