Inversion Theory and Conformal Mapping - Brossura

Blair, David E.

Brossura

ISBN 10: 0821826360 ISBN 13: 9780821826362

Casa editrice: Amer Mathematical Society, 2000

Riassunto

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 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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Product Description

Book by David E Blair

Dettagli dell'edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2000
• Lingua: Inglese
• ISBN 10: 0821826360
• ISBN 13: 9780821826362
• Rilegatura: Copertina flessibile
• Numero di pagine: 118
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile