Newton's lemma XXVIII on integrable ovals in higher dimensions and reflection groups

Newton's lemma XXVIII on integrable ovals in higher dimensions and reflection groups

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 ${{{\mathbb R}}}^2$, this is Lemma XXVIII from Newton's &...

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Veröffentlicht in:The Bulletin of the London Mathematical Society 2015-04, Vol.47 (2), p.290-300
1. Verfasser: Vassiliev, V. A.
Format: Artikel
Sprache:eng
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Zusammenfassung: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 ${{{\mathbb R}}}^2$, this is Lemma XXVIII from Newton's 'Philosophiae naturalis principia mathematica'.
ISSN:0024-6093
1469-2120
DOI:10.1112/blms/bdv002