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• W2298314207 abstract "Harmonic Polynomials and Free Boundary Regularity for Harmonic Measure from Two Sides Matthew Badger Chair of the Supervisory Committee: Professor Tatiana Toro Mathematics We use tools from geometric measure theory to catalog fine behavior of harmonic measure on a class of two-sided domains Ω ⊂ R in n-dimensional Euclidean space, with n ≥ 3. Assume the interior Ω = Ω and exterior Ω− = R Ω of Ω are NTA domains, equipped with harmonic measures ω and ω−, respectively. We prove that if ω and ω− are mutually absolutely continuous and the logarithm of their Radon-Nikodym derivative dω−/dω+ has vanishing mean oscillation, then the boundary ∂Ω can be written as a finite disjoint union of sets Γk (1 ≤ k ≤ d) with the following properties. For each Q ∈ Γk, every blow-up of ∂Ω centered atQ is the zero set of a homogeneous harmonic polynomial of degree k which separates space into two connected components; the set Γ1 of “flat points” is relatively open and locally Reifenberg flat with vanishing constant; and the setΓ2∪· · ·∪Γd of “singularities” has harmonic measure zero." @default.
• W2298314207 created "2016-06-24" @default.
• W2298314207 creator A5089482696 @default.
• W2298314207 date "2011-01-01" @default.
• W2298314207 modified "2023-09-27" @default.
• W2298314207 title "Harmonic Polynomials and Free Boundary Regularity for Harmonic Measure from Two Sides" @default.
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• W2298314207 hasPublicationYear "2011" @default.
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