The critical dimension for the one-phase Bernoulli problem

Formal proof listed 1 paper September 24, 2026
What the paper claims, in its own words

Establishes seven as the first dimension admitting a nonflat, one-homogeneous global minimizer of the one-phase Bernoulli energy. Consequently, minimizing free boundaries are smooth through dimension six, and their singular sets have dimension at most n−7n-7 in higher dimensions.

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The original paper