Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 3-19

DISCRETE REIFENBERG-TYPE THEOREM

Michal Miskiewicz

University of Warsaw, Institute of Mathematics
Banacha 2, 02-097 Warszawa, Poland; m.miskiewicz 'at' mimuw.edu.pl

Abstract. The paper proves that a bound on the averaged Jones' square function of a measure implies an upper bound on the measure. Various types of assumptions on the measure are considered. The theorem is a generalization of a result due to Naber and Valtorta in connection with measure bounds on the singular set of harmonic maps.

2010 Mathematics Subject Classification: Primary 28A75, 28A78.

Key words: Reifenberg parametrization, Jones' square number.

Reference to this article: M. Miskiewicz: Discrete Reifenberg-type theorem. Ann. Acad. Sci. Fenn. Math. 43 (2018), 3-19.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4301