Corpus ID: 119151159

Rigidity, graphs and Hausdorff dimension

@inproceedings{Chatzikonstantinou2017RigidityGA,
  title={Rigidity, graphs and Hausdorff dimension},
  author={N. Chatzikonstantinou and Alex Iosevich and Sevak Mkrtchyan and Jonathan Pakianathan},
  year={2017}
}
  • N. Chatzikonstantinou, Alex Iosevich, +1 author Jonathan Pakianathan
  • Published 2017
  • Mathematics
  • For a compact set $E \subset \mathbb R^d$ and a connected graph $G$ on $k+1$ vertices, we define a $G$-framework to be a collection of $k+1$ points in $E$ such that the distance between a pair of points is specified if the corresponding vertices of $G$ are connected by an edge. We regard two such frameworks as equivalent if the specified distances are the same. We show that in a suitable sense the set of equivalences of such frameworks naturally embeds in ${\mathbb R}^m$ where $m$ is the number… CONTINUE READING

    Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

    Figures from this paper.

    Citations

    Publications citing this paper.

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 33 REFERENCES

    Lectures on Harmonic Analysis

    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL

    Decay of circular means of Fourier transforms of measures

    VIEW 5 EXCERPTS
    HIGHLY INFLUENTIAL

    On the Hausdorff dimensions of distance sets

    VIEW 8 EXCERPTS
    HIGHLY INFLUENTIAL

    Hausdorff dimension and distance sets

    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL

    The Geometry Of Fractal Sets

    VIEW 1 EXCERPT

    The Falconer problem

    • A. Iosevich, B. Liu
    • additive energy and Cartesian products, (http://arxiv.org/pdf/1506.07595.pdf), Finnish Academy of Science and Letters, volume 41
    • 2015
    VIEW 1 EXCERPT