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

Authors: C. Kenig, D. Preiss and T. Toro
Journal: J. Amer. Math. Soc. 22 (2009), 771-796
MSC (2000): Primary 28A33, 31A15
DOI: https://doi.org/10.1090/S0894-0347-08-00601-2
Published electronically: April 25, 2008
MathSciNet review: 2505300
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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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