Calculus of Variations and Geometric Measure Theory

M. Goldman - M. Novaga - B. Ruffini

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

created by ruffini on 19 Apr 2021
modified by novaga on 12 Jan 2022


Published Paper

Inserted: 19 apr 2021
Last Updated: 12 jan 2022

Journal: Proc. Amer. Math. Soc.
Volume: 150
Number: 3
Pages: 1153-1165
Year: 2022

ArXiv: 2104.09851 PDF


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.