Boundary structure and size in terms of interior and exterior harmonic measures in higher dimensions

Kenig, C.; Preiss, D.; Toro, T.

doi:10.1090/S0894-0347-08-00601-2

Boundary structure and size in terms of interior and exterior harmonic measures in higher dimensions
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by C. Kenig, D. Preiss and T. Toro

J. Amer. Math. Soc. 22 (2009), 771-796

DOI: https://doi.org/10.1090/S0894-0347-08-00601-2

Published electronically: April 25, 2008

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Abstract:

In this work we introduce the use of powerful tools from geometric measure theory (GMT) to study problems related to the size and structure of sets of mutual absolute continuity for the harmonic measure $\omega ^+$ of a domain $\Omega =\Omega ^+\subset \mathbb {R}^n$ and the harmonic measure $\omega ^-$ of $\Omega ^-$, $\Omega ^-=\mbox {int}(\Omega ^c)$, in dimension $n\ge 3$.

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