Conformal Geometry and Quasiregular Mappings
Conformal Geometry and Quasiregular Mappings
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DOI：
10.1007/bfb0077904
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发表时间：
1988-05
期刊：
影响因子：
--
通讯作者：
M. Vuorinen
中科院分区：
文献类型：
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作者：
M. Vuorinen
本书是为新手读者介绍的空间拟正则映射理论。同时，本书还针对经典分析，特别是几何函数理论的专家。本书引导读者了解当前研究的前沿，并涵盖了该主题的一些最新进展，这些进展以前分散在文献中。在本专着中，某些保形不变量发挥着重要作用，它们是与曲线族极值长度相关的极值问题的解决方案。然后应用这些不变量来证明拟正则映射的锐畸变定理。这些共形几何的极值问题之一概括了 O. Teichmüller 的经典二维问题。该论述的新颖之处在于应用共形不变量的方式，即使在二维特殊情况下，所获得的清晰结果也应该引起相当大的兴趣。本书结合了教科书和研究专着的特点：这是该主题的第一本英文介绍，包含近百个练习、该主题的调查以及广泛的参考书目，最后还有一个开放问题清单。
This book is an introduction to the theory of spatial quasiregular mappings intended for the uninitiated reader. At the same time the book also addresses specialists in classical analysis and, in particular, geometric function theory. The text leads the reader to the frontier of current research and covers some most recent developments in the subject, previously scatterd through the literature. A major role in this monograph is played by certain conformal invariants which are solutions of extremal problems related to extremal lengths of curve families. These invariants are then applied to prove sharp distortion theorems for quasiregular mappings. One of these extremal problems of conformal geometry generalizes a classical two-dimensional problem of O. Teichmüller. The novel feature of the exposition is the way in which conformal invariants are applied and the sharp results obtained should be of considerable interest even in the two-dimensional particular case. This book combines the features of a textbook and of a research monograph: it is the first introduction to the subject available in English, contains nearly a hundred exercises, a survey of the subject as well as an extensive bibliography and, finally, a list of open problems.