Harmonic Measure

Abstract

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.

Computing Conformal Maps of Finitely Connected Domains onto Canonical Slit Domains

“…However, this is much more generality than we shall need here. The reader who desires this further development can find an outstanding treatment in [8].…”

Compact composition operators with symbol a universal covering map

“…We will not list these here but many of these cane be found in [7] and throughout the literature on compact composition operators.…”

Positive harmonic functions on Denjoy domains in the complex plane

“…We briefly recall the notion of the module of families of curves, generalized in an obvious way to path families, see [1], [17], [23] and [14] for details.…”