Overview

Mikhail Gromov introduced pseudo-holomorphic curves into symplectic geometry in 1985. Since then, pseudo-holomorphic curves have taken on great importance in many fields. The aim of this book is to present the original proof of Gromov's compactness theorem for pseudo-holomorphic curves in detail. Local properties of pseudo-holomorphic curves are investigated and proved from a geometric viewpoint. Properties of particular interest are isoperimetric inequalities, a monotonicity formula, gradient bounds and the removal of singularities. A special chapter is devoted to relevant features of hyperbolic surfaces, where pairs of pants decomposition and thickthin decomposition are described. The book is essentially self-contained and should also be accessible to students with a basic knowledge of differentiable manifolds and covering spaces.

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9783764357351

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    ""...the book provides a self-contained and for the most part excellent elaboration of Gromov's proof of the compactness theorem.""      -- Mathematical Reviews 

...the book provides a self-contained and for the most part excellent elaboration of Gromov's proof of the compactness theorem. -- Mathematical Reviews

"    ""...the book provides a self-contained and for the most part excellent elaboration of Gromov's proof of the compactness theorem.""      -- Mathematical Reviews "

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