A hypersurface containing the support of a Radon transform must be an ellipsoid. I

Jan Boman

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arXiv · 1910.01725

A hypersurface containing the support of a Radon transform must be an ellipsoid. I

Jan Boman

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Abstract

If the Radon transform of a compactly supported distribution $f \ne 0$ in $\mathbb R^n$ is supported on the set of tangent planes to the boundary $\partial D$ of a bounded convex domain $D$, then $\partial D$ must be an ellipsoid. As a corollary of this result we get a new proof of a recent theorem of Koldobsky, Merkurjev, and Yaskin, which settled a special case of a conjecture of Arnold that was motivated by a famous lemma of Newton.

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Jan Boman. 2019-10-03. A hypersurface containing the support of a Radon transform must be an ellipsoid. I. https://arxiv.org/abs/1910.01725

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