论文标题
奇数空间中的可集成体
Integrable bodies in odd-dimensional spaces
论文作者
论文摘要
V. Arnold的问题1987-14询问$ r^n $（奇数空间中的圆锥形除外）是否存在光滑的超曲面，任何超平面从体体中切除的片段的体积是由这种超脉冲界定的，这是增生的代数功能。我们对这种新的超曲面的作用非常现实：特别是，它是此类Hypersurfaces的示例（另外是Archimedes的圆锥）的例子，为此，该体积函数的分析延续是有限的。
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.
