Gromov’s Compactness Theorem for Pseudo-holomorphic Curves
Gromov’s Compactness Theorem for Pseudo-holomorphic Curves
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伪全纯曲线的格罗莫夫紧性定理
DOI：
10.1007/978-3-0348-8952-0
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发表时间：
2004
影响因子：
2.5
通讯作者：
Christoph Hummel
中科院分区：
文献类型：
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作者：
Christoph Hummel
米哈伊尔·格罗莫夫在1985年将伪全纯曲线引入辛几何。这本书的目的是详细介绍原始证明格罗莫夫的紧凑性定理的伪全纯曲线。从几何角度研究并证明了伪全纯曲线的局部性质。特别感兴趣的性质是等周不等式、单调性公式、梯度界和奇异点的去除。一个特殊的章节是专门的双曲曲面，厚薄分解描述的相关功能。这篇文章应该是可访问的学生与微分流形和覆盖空间的基本知识。
Mikhail Gromov introduced pseudo-holomorphic curves into symplectic geometry in 1985. This book aims to present in detail the original proof for Gromov's compactness theorum for pseudo-holomorphic curves. 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 thick-thin decomposition is described. This text should be accessible to students with a basic knowledge of differentiable manifolds and covering spaces.