Abstract
Let K be a bounded body in Rn, n is odd, with infinitely smooth boundary. We prove that if the volume cut off from the body by a hyperplane is a free of real singularities algebraic function of the parameters of the hyperplane then the body is an ellipsoid. This partially answers a question of V.I. Arnold: whether odd-dimensional ellipsoids are the only algebraically integrable bodies?.
| Original language | English |
|---|---|
| Title of host publication | Contemporary Mathematics |
| Publisher | American Mathematical Society |
| Pages | 33-44 |
| Number of pages | 12 |
| DOIs | |
| State | Published - 2019 |
Publication series
| Name | Contemporary Mathematics |
|---|---|
| Volume | 733 |
| ISSN (Print) | 0271-4132 |
| ISSN (Electronic) | 1098-3627 |
Bibliographical note
Publisher Copyright:©2019 American Mathematical Society.