| Abstract: |
| We give an example of a pair of nonnegative subharmonic functions with disjoint support for which the Alt-Caffarelli-Friedman (ACF) monotonicity formula has strictly positive limit at the origin, and yet the interface between the supports lacks a tangent at the origin. I will also discuss a quantitative stability result for the ACF monotonicity formula. This is joint work with Dennis Kriventsov and Robin Neumayer. |
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