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arXiv · 1109.1427

Flat points in zero sets of harmonic polynomials and harmonic measure from two sides

Matthew Badger
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Abstract

We obtain quantitative estimates of local flatness of zero sets of harmonic polynomials. There are two alternatives: at every point either the zero set stays uniformly far away from a hyperplane in the Hausdorff distance at all scales or the zero set becomes locally flat on small scales with arbitrarily small constant. An application is given to a free boundary problem for harmonic measure from two sides, where blow-ups of the boundary are zero sets of harmonic polynomials.

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Matthew Badger. 2012-04-26. Flat points in zero sets of harmonic polynomials and harmonic measure from two sides. https://doi.org/10.1112/jlms%2Fjds041

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