John B. Garnett

Harmonic Measure (eBook, PDF)

• Format: PDF

Produktbeschreibung

During the last two decades several remarkable new results were discovered about harmonic measure in the complex plane. This book provides a careful survey of these results and an introduction to the branch of analysis which contains them. Many of these results, due to Bishop, Carleson, Jones, Makarov, Wolff and others, appear here in paperback for the first time. The book is accessible to students who have completed standard graduate courses in real and complex analysis. The first four chapters provide the needed background material on univalent functions, potential theory, and extremal length, and each chapter has many exercises to further inform and teach the readers.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 4. April 2005
• Englisch
• ISBN-13: 9780511406331
• Artikelnr.: 38185555

Autorenporträt

John B. Garnett is Professor of Mathematics in the Department of Mathematics at University of California, Los Angeles.

Inhaltsangabe

1. Jordan domains; 2. Finitely connected domains; 3. Potential theory; 4. Extremal distance; 5. Applications and reverse inequalities; 6. Simply connected domains, part one; 7. Bloch functions and quasicircles; 8. Simply connected domains, part two; 9. Infinitely connected domains; 10. Rectifiability and quadratic expressions; Appendices.

Rezensionen

'The authors say that they wrote this book to explain the exciting new developments in the subject over the past couple of decades. They have achieved this with an impressive scholarship and outstanding expository clarity. ... it has clearly been written with great care and deep insight into the subject matter. I expect it to become a highly valued addition to the bookshelves of students and experienced researchers alike.' Zentralblatt MATH