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arXiv · 1407.7221

There are no algebraically integrable ovals in even-dimensional spaces

Victor A. Vassiliev
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Abstract

We prove that there are no bounded domains with smooth boundaries in even-dimensional Euclidean spaces, such that the volumes cut off from them by affine hyperplanes depend algebraically on these hyperplanes. For convex ovals in $R^2$, this is Lemma XXVIII from Newton's "Principia".

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Victor A. Vassiliev. 2014-07-27. There are no algebraically integrable ovals in even-dimensional spaces. https://arxiv.org/abs/1407.7221

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