Integrable bodies in odd-dimensional spaces
Algebraic Geometry
2020-03-31 v2
Abstract
V. Arnold's problem 1987-14 asks whether there exist smooth hypersurfaces in (other than the conics in odd-dimensional spaces) for which the volume of the segment cut by any hyperplane from the body bounded by such a hypersurface is an algebraic function of the hyperplane. We desribe very realistic candidates for the role of such new hypersurfaces: in particular, it are examples (additional to Archimedes' conics) of such hypersurfaces, for which the analytic continuation of this volume function is finitely valued.
Cite
@article{arxiv.2003.04665,
title = {Integrable bodies in odd-dimensional spaces},
author = {V. A. Vassiliev},
journal= {arXiv preprint arXiv:2003.04665},
year = {2020}
}