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arXiv · 2003.04665

Integrable bodies in odd-dimensional spaces

V. A. Vassiliev
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Abstract

V. Arnold's problem 1987-14 asks whether there exist smooth hypersurfaces in $R^N$ (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.

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V. A. Vassiliev. 2020-03-10. Integrable bodies in odd-dimensional spaces. https://arxiv.org/abs/2003.04665

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