Аннотация
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.
Язык оригинала | английский |
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Страницы (с-по) | 480-484 |
Число страниц | 5 |
Журнал | Doklady Mathematics |
Том | 100 |
Номер выпуска | 2 |
DOI | |
Состояние | Опубликовано - 1 сент. 2019 |