Calculus of Variations and Geometric Measure Theory
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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 20 Jun 2021


Accepted Paper

Inserted: 19 apr 2021
Last Updated: 20 jun 2021

Journal: Proc. Amer. Math. Soc.
Year: 2021

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.


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