Uniform rectifiability, bounded harmonic functions, and elliptic PDE's

In this talk I will describe a recent characterization of uniform rectifiability in terms of a variant of the so called area function (or g function) for harmonic functions and an analogous result involving solutions of elliptic PDE's. As a byproduct, we obtain a new characterization of uniform rectifiability in terms of harmonic measure or elliptic measure. Some of these results are joint work with Azzam, Garnett and Mourgoglou

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