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Doklady Mathematics

, Volume 100, Issue 2, pp 480–484 | Cite as

Sharp Estimates for Geometric Rigidity of Isometries on the First Heisenberg Group

  • D. V. IsangulovaEmail author
MATHEMATICS
  • 4 Downloads

Abstract

We prove the quantitative stability of isometries on the first Heisenberg group with sub-Riemannian geometry: every \((1 + \varepsilon )\)-quasi-isometry of the John domain of the Heisenberg group \(\mathbb{H}\) is close to some isometry with the order of closeness \(\sqrt \varepsilon + \varepsilon \) in the uniform norm and with the order of closeness \(\varepsilon \) in the Sobolev norm. An example demonstrating the asymptotic sharpness of the results is given.

Notes

FUNDING

This work was supported by the Ministry of Education and Science of the Russian Federation, project no. 1.3087.2017/4.6.

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Novosibirsk State UniversityNovosibirskRussia

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