Reifenberg flatness for almost-minimizers of the perimeter under minimal assumptions

Michael Goldman (1) , Matteo Novaga , Berardo Ruffini

1 LJLL - Laboratoire Jacques-Louis Lions

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 excess at some scale implies smallness of the excess at all smaller scales.

Domaines: Equations aux dérivées partielles [math.AP]

Michael Goldman, Matteo Novaga, Berardo Ruffini. Reifenberg flatness for almost-minimizers of the perimeter under minimal assumptions. Proceedings of the American Mathematical Society, 2022. ⟨hal-03202272v2⟩