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arxiv: 0910.2591 · v1 · pith:4XUD5YVEnew · submitted 2009-10-14 · 🧮 math.AP · math.CA

Harmonic polynomials and tangent measures of harmonic measure

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keywords harmonicmeasurepolynomialstangentassociatedboundaryderiveddomain
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We show that on an NTA domain if each tangent measure to harmonic measure at a point is a polynomial harmonic measure then the associated polynomials are homogeneous. Geometric information for solutions of a two-phase free boundary problem studied by Kenig and Toro is derived.

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