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

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.

arXiv comment17 pages