On algebraically integrable bodies

Mark Agranovsky

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

5 Scopus citations


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 languageEnglish
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Number of pages12
StatePublished - 2019

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Bibliographical note

Publisher Copyright:
©2019 American Mathematical Society.


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