Open AccessSharp estimates of the geometric rigidity on the first Heisenberg group
Author(s) -
Д. В. Исангулова,
Д. В. Исангулова
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-56524886590-594
Subject(s) - heisenberg group , mathematics , rigidity (electromagnetism) , closeness , norm (philosophy) , isometry (riemannian geometry) , pure mathematics , sobolev space , isometry group , group (periodic table) , order (exchange) , mathematical analysis , physics , quantum mechanics , political science , law , finance , economics
We prove quantitative stability of isometries on the first Heisenberg group with sub-Riemannian geometry: every (1 + )-quasi-isometry of the John domain of the Heisenberg group is close to some isometry with order of closeness in the uniform norm and with the order of closeness+ in the Sobolev norm. An example demonstrating the asymptotic sharpness of the results is given.