Sharp Estimates for Geometric Rigidity of Isometries on the First Heisenberg Group
- Autores: Isangulova D.1
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Afiliações:
- Novosibirsk State University
- Edição: Volume 100, Nº 2 (2019)
- Páginas: 480-484
- Seção: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225726
- DOI: https://doi.org/10.1134/S1064562419050235
- ID: 225726
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Resumo
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.
Sobre autores
D. Isangulova
Novosibirsk State University
Autor responsável pela correspondência
Email: d.isangulova@g.nsu.ru
Rússia, Novosibirsk, 630090