Applications of Harmonic Measure (The University of Arkansas Lecture Notes in the Mathematical Sciences) by John B. GarnettMy rating: 3 of 5 stars
Typesetting of the book is more of 70s Soviet Russia rather than the first world of the 80s. As clearly indicated in the title, the book is not about Harmonic measures but rather their applications. Still, it is one of the better introductions to them, perhaps only Conformal Invariants: Topics in Geometric Function Theory was a better book explaining them when it was written (and which, to be fair, I only discovered for Garnett cites them here). Only Krantz's The Theory and Practice of Conformal Geometry beats both of them. Garnett's own Harmonic Measure couauther many years later is not good either.
The approach is purely deterministic, but a small introduction is made to the probabilistic approach and references are provided should one be interested. The applications are interesting, but in case they are in Krantz's or Ahlfors' books, the exposition there is better. Still, a many of the applications first (and in a couple of cases only time) appeared in monograph form here and as such the book has its value.
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