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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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    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.2012-11-12

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