# 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} }

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

#### Citations

##### Publications citing this paper.

SHOWING 1-2 OF 2 CITATIONS

## Finite Point Configurations in the Plane, Rigidity and Erdős Problems

VIEW 1 EXCERPT

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 33 REFERENCES

## A bilinear Fourier extension theorem and applications to the distance set problem

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## 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

## On polynomial configurations in fractal sets

VIEW 1 EXCERPT

## The Geometry Of Fractal Sets

VIEW 1 EXCERPT

## Fourier Analysis and Hausdorff Dimension

VIEW 1 EXCERPT

## The Falconer problem

VIEW 1 EXCERPT

## Finite Chains inside Thin Subsets of ${\Bbb R}^d$

VIEW 1 EXCERPT