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商品詳細
Gromov's Compactness Theorem for Pseudo-holomorphic Curves. Softcover reprint of the original 1st ed. 1997.
・ISBN 978-3-0348-9842-3 paper EUR 49.99
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| 著者・編者 | Hummel, Christoph, |
|---|---|
| シリーズ | Progress in Mathematics |
| 出版社 | (Springer Basel, SZ) |
| 出版年月 | 2012 |
| ページ数 | 135 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-17643＞ |
解説
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.