Integrable bodies in odd-dimensional spaces

2020/03/10 by Vassiliev, V. A.
#44A99 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.04665

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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