3 0 N ov 2 00 7 Confirmation of Matheron ’ s Conjecture on the Covariogram of a Planar Convex Body

@inproceedings{Averkov200730N,
  title={3 0 N ov 2 00 7 Confirmation of Matheron ’ s Conjecture on the Covariogram of a Planar Convex Body},
  author={Gennadiy Averkov and Gabriele Bianchi},
  year={2007}
}
The covariogram gK of a convex body K in E d is the function which associates to each x ∈ E d the volume of the intersection of K with K + x. In 1986 G. Matheron conjectured that for d = 2 the covariogram gK determines K within the class of all planar convex bodies, up to translations and reflections in a point. This problem is equivalent to some problems in stochastic geometry and probability as well as to a particular case of the phase retrieval problem in Fourier analysis. It is also… CONTINUE READING

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