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math.AP2023
Cantor sets with absolutely continuous harmonic measure
Guy David, Cole Jeznach, Antoine Julia
We construct Ahlfors regular Cantor sets of small dimension in the plane, such that the Hausdorff measure on is equivalent to the harmonic measure associated to its complem…
math.AP2020★ 1 cited
Uniform energy distribution in a pattern-forming system of surface charges
Katarina Bellova, Antoine Julia, Felix Otto
We consider a variational model for a charge density on a (hyper)plane, with a short-range attraction coming from the interfacial energy and a long-range repulsion c…