Gromov's Compactness Theorem for Pseudo-holomorphic Curves
By: by Christoph Hummel
Series: Progress in Mathematics -- 151; Progress in Mathematics -- 151
Publisher: Birkhäuser Basel; Imprint: Birkhäuser
Published: 1997
Place of publication: Basel
Language: eng
Format: [electronic resource] /
Number of pages: 135
ISBN-13: 9783034898423; 9783034889520
Subjects: Mathematics
Description: 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.
Notes: Online full text is restricted to subscribers.

Also available in print.

Mode of access: World Wide Web.