Sharp geometric rigidity of isometries on Heisenberg groups

Sharp geometric rigidity of isometries on Heisenberg groups Full article

Journal

Mathematische Annalen
ISSN: 0025-5831 , E-ISSN: 1432-1807

Output data

Year: 2012, Volume: 355, Pages: 1301–1329 Pages count : 28 DOI: 10.1007/s00208-012-0820-2

Authors

Isangulova D.V. ¹ , Vodopyanov S.K. ¹

Affiliations

1	Sobolev Institute of Mathematics SB RAS, 4 Acad. Koptyug Avenue, 630090 Novosibirsk, Russia

We prove sharp geometric rigidity estimates for isometries on Heisenberg groups. Our main result asserts that every (1 + ε)-quasi-isometry on a John domain of the Heisenberg group H^n, n > 1, is close to some isometry up to proximity order √ ε + ε in the uniform norm, and up to proximity order ε in the L^1_p-norm. We give examples showing the asymptotic sharpness of our results.

Isangulova D.V. , Vodopyanov S.K.
Sharp geometric rigidity of isometries on Heisenberg groups
Mathematische Annalen. 2012. V.355. P.1301–1329. DOI: 10.1007/s00208-012-0820-2 WOS Scopus OpenAlex

Submitted:	Apr 6, 2009
Published online:	Jun 14, 2012

≡ Web of science:	WOS:000316870300004
≡ Scopus:	2-s2.0-84875591243
≡ OpenAlex:	W2053721593