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About this book
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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Table of contents (7 chapters)
Reviews
"...the book provides a self-contained and for the most part excellent elaboration of Gromov's proof of the compactness theorem."
-- Mathematical Reviews
Authors and Affiliations
Bibliographic Information
Book Title: Gromov’s Compactness Theorem for Pseudo-holomorphic Curves
Authors: Christoph Hummel
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-3-0348-8952-0
Publisher: Birkhäuser Basel
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eBook Packages: Springer Book Archive
Copyright Information: Springer Basel 1997
Hardcover ISBN: 978-3-7643-5735-1Published: 01 May 1997
Softcover ISBN: 978-3-0348-9842-3Published: 15 October 2012
eBook ISBN: 978-3-0348-8952-0Published: 06 December 2012
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: VIII, 135
Topics: Geometry