Corpus ID: 202734319

Geometric criteria for $C^{1,\alpha}$ rectifiability.

@inproceedings{Nin2019GeometricCF,
  title={Geometric criteria for \$C^\{1,\alpha\}\$ rectifiability.},
  author={Giacomo Del Nin and Kennedy Obinna Idu},
  year={2019}
}
  • Giacomo Del Nin, Kennedy Obinna Idu
  • Published 2019
  • Mathematics
  • We prove criteria for $\mathcal{H}^k$-rectifiability of subsets of $\mathbb{R}^n$ with $C^{1,\alpha}$ maps, $0<\alpha\leq 1$, in terms of suitable approximate tangent paraboloids. We also provide a version for the case when there is not an a priori tangent plane, measuring on dyadic scales how close the set is to lying in a $k$-plane. We then discuss the relation with similar criteria involving Peter Jones' $\beta$ numbers, in particular proving that a sufficient condition is the boundedness… CONTINUE READING

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