Inversion Theory and Conformal Mapping pdf epub mobi txt 电子书下载 2025

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David E. Blair: Michigan State University, East Lansing, MI

出版者:American Mathematical Society

作者:David E. Blair

出品人:

页数:118

译者:

出版时间:2000-8-17

价格:USD 22.00

装帧:Paperback

isbn号码:9780821826362

丛书系列:Student Mathematical Library

图书标签:

数学
微分几何7
反演理论
共形映射

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It is rarely taught in undergraduate or even graduate curricula that the only conformal maps in Euclidean space of dimension greater than two are those generated by similarities and inversions in spheres. This is in stark contrast to the wealth of conformal maps in the plane. This fact is taught in most complex analysis courses.

The principal aim of this text is to give a treatment of this paucity of conformal maps in higher dimensions. The exposition includes both an analytic proof, due to Nevanlinna, in general dimension and a differential geometric proof in dimension three. For completeness, enough complex analysis is developed to prove the abundance of conformal maps in the plane. In addition, the book develops inversion theory as a subject, along with the auxiliary theme of circle-preserving maps. A particular feature is the inclusion of a paper by Carathéodory with the remarkable result that any circle-preserving transformation is necessarily a Möbius transformation—not even the continuity of the transformation is assumed.

The text is at the level of advanced undergraduates and is suitable for a capstone course, topics course, senior seminar or as an independent study text. Students and readers with university courses in differential geometry or complex analysis bring with them background to build on, but such courses are not essential prerequisites.