Siberian Mathematical Journal

, Volume 59, Issue 6, pp 1090–1093 | Cite as

The Monge Problem of “Piles and Holes” on the Torus and the Problem of Small Denominators

  • V. V. KozlovEmail author


We discuss the problem of existence of a smooth endomorphism of a closed n-dimensional manifold carrying a differential n-form into a prescribed volume form. Of course, we assume that the integrals of these forms over the whole manifold are equal. The solution of this problem for the n-dimensional torus reduces to the problem of small denominators well known in analysis.


Monge–Kantorovich problem smooth endomorphisms small denominators 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Steklov Institute of MathematicsMoscowRussia

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