The branching set of 2D two-phase Bernoulli free boundaries with constant coefficients is locally finite.
An allard-type boundary regularity theorem for $2d$minimizing currents at smooth curves with arbitrary multiplicity.Publications math´ ematiques de l’IH´ES
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Fine structure of the two-phase Bernoulli free boundaries in 2D
The branching set of 2D two-phase Bernoulli free boundaries with constant coefficients is locally finite.