Harmonic Measure [Hardcover]

An introduction to harmonic measure on plane domains and careful discussion of the work of Makarov, Carleson, Jones and others.This book provides a careful survey of the remarkable new results about harmonic measure in the complex plane, and an introduction to harmonic measure on plane domains. Many results, due to Bishop, Carleson, Jones, Makarov, Wolff, Bertilsson, Pommerenke and others, appear here in paperback for the first time.This book provides a careful survey of the remarkable new results about harmonic measure in the complex plane, and an introduction to harmonic measure on plane domains. Many results, due to Bishop, Carleson, Jones, Makarov, Wolff, Bertilsson, Pommerenke and others, appear here in paperback for the first time.This book provides an enlightening survey of remarkable new results that have only recently been discovered in the past two decades about harmonic measure in the complex plane. 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. ...everybody who is interested in function theory and for whom Harmonic Measure sounds somewhat familiar and potentially interesting will find this book extremely useful, wonderfully well written and a joy to read.
MAA Reviews Over the last 20 years I have often been asked to suggest ló(