Abstract
We prove that the geometric covariogram determines (up to translation and reflection), among all convex bodies, any plane convex body which is $C^2$ and has positive curvature everywhere. This gives a partial answer to a problem posed by G. Matheron.
Citation
Gabriele Bianchi. Fausto Segala. Aljoša Volčič. "The Solution of the Covariogram Problem for Plane $\mathcal{C}^2_+$ Convex Bodies." J. Differential Geom. 60 (2) 177 - 198, February, 2002. https://doi.org/10.4310/jdg/1090351101
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