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

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Abstract

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

Original languageEnglish
Pages (from-to)480-484
Number of pages5
JournalDoklady Mathematics
Volume100
Issue number2
DOIs
Publication statusPublished - 1 Sep 2019

Keywords

  • BOUNDED DISTORTION
  • MAPPINGS
  • STABILITY

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