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}
}
• 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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#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 23 REFERENCES

## Conditions quantitatives de rectifiabilité

VIEW 1 EXCERPT
HIGHLY INFLUENTIAL

## C-rectifiable sets

• G. Anzellotti, R. Serapioni
• J. Reine Angew. Math, 453:1–20
• 1994
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

## Menger curvatures and $C^{1,\alpha}$ rectifiability of measures

• Mathematics
• 2019

## Characterization of rectifiable measures in terms of $\alpha$-numbers

• Mathematics
• 2018
VIEW 1 EXCERPT

## Sufficient conditions for C parametrization and rectifiability

VIEW 2 EXCERPTS

## Higher order rectifiability of measures via averaged discrete curvatures

• S. Kolasiński
• Rev. Mat. Iberoam., 33(3):861–884
• 2017

## Rectifiability and approximate differentiability of higher order for sets

VIEW 1 EXCERPT

## Wasserstein distance and the rectifiability of doubling measures: part I

• Mathematics
• 2016
VIEW 1 EXCERPT

## Characterization of n-rectifiability in terms of Jones’ square function: Part II

• Mathematics
• 2015