Harmonic Measure

An introduction to harmonic measure on plane domains and careful discussion of the work of Makarov, Carleson, Jones and others.

John B. Garnett (Author), Donald E. Marshall (Author)

9780521470186, Cambridge University Press

Hardback, published 4 April 2005

588 pages, 126 b/w illus. 1 table 190 exercises
23.6 x 16.3 x 4.2 cm, 0.89 kg

'… can be warmly recommended to students and researchers with a deep interest in analysis. It is an excellent preparation for serious work in complex analysis or potential theory.' EMS Newsletter

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.

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.

Subject Areas: Complex analysis, complex variables [PBKD]