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    Inversion Theory and Conformal Mapping (Student Mathematical Library, V. 9) (Paperback) By (author) David E. Blair

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    DescriptionIt 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 Caratheodory with the remarkable result that any circle-preserving transformation is necessarily a Mobius 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.


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  • Full bibliographic data for Inversion Theory and Conformal Mapping

    Title
    Inversion Theory and Conformal Mapping
    Authors and contributors
    By (author) David E. Blair
    Physical properties
    Format: Paperback
    Number of pages: 118
    Width: 135 mm
    Height: 211 mm
    Thickness: 13 mm
    Weight: 113 g
    Language
    English
    ISBN
    ISBN 13: 9780821826362
    ISBN 10: 0821826360
    Classifications

    BIC E4L: MAT
    Nielsen BookScan Product Class 3: S7.8
    B&T Book Type: NF
    B&T Merchandise Category: TXT
    B&T Modifier: Region of Publication: 01
    B&T General Subject: 710
    B&T Modifier: Academic Level: 02
    B&T Modifier: Text Format: 06
    BISAC V2.8: MAT000000
    DC21: 516.36
    BIC subject category V2: PBMP
    DC22: 516.3/6
    LC subject heading: ,
    LC classification: QA473 .B57 2000
    Thema V1.0: PBMP
    Illustrations note
    bibliography, index
    Publisher
    American Mathematical Society
    Imprint name
    American Mathematical Society
    Publication date
    01 September 2000
    Publication City/Country
    Providence
    Table of contents
    Classical inversion theory in the plane Linear fractional transformations Advanced calculus and conformal maps Conformal maps in the plane Conformal maps in Euclidean space The classical proof of Liouville's theorem When does inversion preserve convexity? Bibliography Index.