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math.AP2017
Dahlberg's theorem in higher co-dimension
Guy David, Joseph Feneuil, Svitlana Mayboroda
In 1977 the celebrated theorem of B. Dahlberg established that the harmonic measure is absolutely continuous with respect to the Hausdorff measure on a Lipschitz graph of dimension…
math.AP2017
Elliptic theory for sets with higher co-dimensional boundaries
Guy R. David, Joseph Feneuil, Svitlana Mayboroda
Many geometric and analytic properties of sets hinge on the properties of harmonic measure, notoriously missing for sets of higher co-dimension. The aim of this manuscript is to de…