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Gromov's Compactness Theorem for Pseudo-Holomorphic Curves
Paperback
Series: Progress in Mathematics, Book 151
ISBN13: 9783034898423
Publisher: Springer Nature
Published: Oct 15 2012
Pages: 135
Weight: 0.48
Height: 0.32 Width: 6.14 Depth: 9.21
Language: English
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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