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math.AP2021
A quantitative stability inequality for fractional capacities
Eleonora Cinti, Roberto Ognibene, Berardo Ruffini
The aim of this work is to show a non-sharp quantitative stability version of the fractional isocapacitary inequality. In particular, we provide a lower bound for the isocapacitary…
math.AP2021
Reifenberg flatness for almost-minimizers of the perimeter under minimal assumptions
Michael Goldman, Matteo Novaga, Berardo Ruffini
The aim of this note is to prove that almost-minimizers of the perimeter are Reifenberg flat, for a very weak notion of minimality. The main observation is that smallness of the ex…