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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

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
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^-=$int$ (\Omega^c)$, in dimension $ n\ge 3$.


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Additional Information

C. Kenig
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: cek@math.uchicago.edu

D. Preiss
Affiliation: Mathematics Institut, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: d.preiss@warwick.ac.uk

T. Toro
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195-4350.
Email: toro@math.washington.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-08-00601-2
PII: S 0894-0347(08)00601-2
Received by editor(s): October 25, 2007
Published electronically: April 25, 2008
Additional Notes: The first author was partially supported by NSF grant DMS-0456583.
The third author was partially supported by NSF grant DMS-0600915
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.