The Monge Problem of “Piles and Holes” on the Torus and the Problem of Small Denominators
- Authors: Kozlov V.V.1
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Affiliations:
- Steklov Institute of Mathematics
- Issue: Vol 59, No 6 (2018)
- Pages: 1090-1093
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172116
- DOI: https://doi.org/10.1134/S0037446618060113
- ID: 172116
Cite item
Abstract
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.
About the authors
V. V. Kozlov
Steklov Institute of Mathematics
Author for correspondence.
Email: kozlov@pran.ru
Russian Federation, Moscow