On algebraically integrable bodies

Mark Agranovsky

doi:10.1090/conm/733/14731

On algebraically integrable bodies

Mark Agranovsky

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

8 Scopus citations

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	https://doi.org/10.1090/conm/733/14731
State	Published - 2019

Publication series

Name	Contemporary Mathematics
Volume	733
ISSN (Print)	0271-4132
ISSN (Electronic)	1098-3627

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Publisher Copyright:
©2019 American Mathematical Society.

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10.1090/conm/733/14731

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On algebraically integrable bodies

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