There are no algebraically integrable ovals in even-dimensional spaces
Algebraic Geometry
2014-07-29 v1
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 , this is Lemma XXVIII from Newton's "Principia".
Keywords
Cite
@article{arxiv.1407.7221,
title = {There are no algebraically integrable ovals in even-dimensional spaces},
author = {Victor A. Vassiliev},
journal= {arXiv preprint arXiv:1407.7221},
year = {2014}
}