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.
Cite this article
Matthew Badger, Harmonic polynomials and tangent measures of harmonic measure. Rev. Mat. Iberoam. 27 (2011), no. 3, pp. 841–870DOI 10.4171/RMI/654