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I recently came across a question concerning harmonic measure here, and was wondering if there is a good reference summarizing different methods of estimating harmonic measure? Specifically, I would be interested in special cases like a sharp estimate for convex domains or other domain types.

I found the general Principle of Extension of Domain here (also called Carleman's Principle of Monotoneity), however the bound presented there is not optimal according to the source: R. Nevanlinna, "Analytic functions".

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This is possibly not much help, but I recently acquired a copy of this book which is entirely about Harmonic Measure, which looks very good indeed. Unfortunately, I have only read the first chapter so far and do not have the book to hand, so can't guarantee that will help with estimating harmonic measure. – Old John Nov 7 '12 at 14:35
Thanks for the comment- I managed to solve my problem using the book and some references. There's a chapter on estimating Harmonic Measure in there. – rngantner Nov 12 '12 at 7:29

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