Metric Spaces, Convexity and Nonpositive Curvature
Metric Spaces, Convexity and Nonpositive Curvature
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DOI：
10.4171/132
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发表时间：
2004-12
期刊：
影响因子：
--
通讯作者：
A. Papadopoulos
中科院分区：
文献类型：
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作者：
A. Papadopoulos
这是2005年出版的一本书的第二版。新版本是一个扩展和修订版本。这本书是关于度量空间的非正曲率意义上的Busemann，即度量空间的距离函数是凸的。我们还系统地介绍了度量空间中的测地线理论和相关问题，并详细介绍了凸性理论的一些方面，这些方面在非正曲率的研究中很有用。论述从第一原理开始，我们给出充分的证明。例子和应用遍布全书，他们来自双曲几何，从理论的Teichmuller空间和希尔伯特几何。在每一章的结尾都有历史注释和其他关于进一步发展的注释。
This is the second edition of a book which appeared in 2005. The new edition is an expanded and revised version. The book is about metric spaces of nonpositive curvature in the sense of Busemann, that is, metric spaces whose distance function is convex. We have also included a systematic introduction to the theory of geodesics and related matters in metric spaces, as well as a detailed presentation of a few facets of convexity theory that are useful in the study of nonpositive curvature. The exposition starts from first principles and we give full proofs. Examples and applications are spread throughout the book, and they come from hyperbolic geometry, from the theory of Teichmuller spaces and from Hilbert geometry. At the end of each chapter there are historical notes and other notes on further developments.