Gromov¿s Compactness Theorem for Pseudo-holomorphic Curves
| Autor: | Hummel, Christoph |
|---|---|
| EAN: | 9783034898423 |
| Sachgruppe: | Mathematik |
| Sprache: | Englisch |
| Seitenzahl: | 148 |
| Produktart: | Kartoniert / Broschiert |
| Veröffentlichungsdatum: | 15.10.2012 |
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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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