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

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Sharp Estimates for Geometric Rigidity of Isometries on the First Heisenberg Group. / Isangulova, D. V.

In: Doklady Mathematics, Vol. 100, No. 2, 01.09.2019, p. 480-484.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{9a474d2acd72429cb4297c91781c4865,

title = "Sharp Estimates for Geometric Rigidity of Isometries on the First Heisenberg Group",

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.",

keywords = "BOUNDED DISTORTION, MAPPINGS, STABILITY",

author = "Isangulova, {D. V.}",

note = "Publisher Copyright: {\textcopyright} 2019, Pleiades Publishing, Ltd.",

year = "2019",

month = sep,

day = "1",

doi = "10.1134/S1064562419050235",

language = "English",

volume = "100",

pages = "480--484",

journal = "Doklady Mathematics",

issn = "1064-5624",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - Sharp Estimates for Geometric Rigidity of Isometries on the First Heisenberg Group

AU - Isangulova, D. V.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - 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.

AB - 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.

KW - BOUNDED DISTORTION

KW - MAPPINGS

KW - STABILITY

UR - http://www.scopus.com/inward/record.url?scp=85075128974&partnerID=8YFLogxK

U2 - 10.1134/S1064562419050235

DO - 10.1134/S1064562419050235

M3 - Article

AN - SCOPUS:85075128974

VL - 100

SP - 480

EP - 484

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 2

ER -

ID: 22337701