Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 693-721
RWTH Aachen University,
Institut für Mathematik
Templergraben 55, D-52062 Aachen, Germany;
kaefer 'at' instmath.rwth-aachen.de
Abstract. We provide a Reifenberg type characterization for m-dimensional C1-submanifolds of Rn. This characterization is also equivalent to Reifenberg-flatness with vanishing constant combined with suitably converging approximating m-planes. Moreover, a sufficient condition can be given by the finiteness of the integral of the quotient of θ(r)-numbers and the scale r, and examples are presented to show that this last condition is not necessary.
2010 Mathematics Subject Classification: Primary 28A75, 53A07, 53C40.
Key words: Reifenberg-flatness, submanifolds, Grassmannian.
Reference to this article: B. Käfer: A Reifenberg type characterization for m-dimensional C1-submanifolds of Rn. Ann. Acad. Sci. Fenn. Math. 44 (2019), 693-721.
https://doi.org/10.5186/aasfm.2019.4443
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