| Abstract: |
| We study the interfacial regularity between a pair of nonnegative subharmonic functions with disjoint positivity sets. The portion of the interface where the Alt-Caffarelli-Friedman (ACF) monotonicity formula is asymptotically positive forms an $\mathcal{H}^{n-1}$ rectifiable set. Moreover, for $\mathcal{H}^{n-1}$-a.e. such point, the two functions have unique blowups, i.e. the Lipschitz rescaling converge in $W^{1,2}$ to a pair of non degenerate truncated linear functions whose supports meet at the approximate tangent plane. |
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