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Box-Quasimetrics and Horizontal Joinability on Cartan Groups. / Greshnov, A. V.; Kostyrkin, V. S.

In: Algebra and Logic, Vol. 1, No. 63, 21.12.2024, p. 10-20.

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

Harvard

Greshnov, AV & Kostyrkin, VS 2024, 'Box-Quasimetrics and Horizontal Joinability on Cartan Groups', Algebra and Logic, vol. 1, no. 63, pp. 10-20. https://doi.org/10.1007/s10469-024-09767-w

APA

Greshnov, A. V., & Kostyrkin, V. S. (2024). Box-Quasimetrics and Horizontal Joinability on Cartan Groups. Algebra and Logic, 1(63), 10-20. https://doi.org/10.1007/s10469-024-09767-w

Vancouver

Greshnov AV, Kostyrkin VS. Box-Quasimetrics and Horizontal Joinability on Cartan Groups. Algebra and Logic. 2024 Dec 21;1(63):10-20. doi: 10.1007/s10469-024-09767-w

Author

Greshnov, A. V. ; Kostyrkin, V. S. / Box-Quasimetrics and Horizontal Joinability on Cartan Groups. In: Algebra and Logic. 2024 ; Vol. 1, No. 63. pp. 10-20.

BibTeX

@article{56b2b5f1e06c4034989a82929efcb7e7,
title = "Box-Quasimetrics and Horizontal Joinability on Cartan Groups",
abstract = "On a Cartan group K equipped with a Carnot–Carath{\'e}odory metric dcc, we find the exact value of a constant in the (1, q2)-generalized triangle inequality for its Box-quasimetric. It is proved that any two points x, y ∈ K can be joined by a horizontal k-broken line Lx,yk, k ≤ 6; moreover, the length of such a broken line Lx,yk does not exceed the quantity Cdcc(x, y) for some constant C not depending on the choice of x, y ∈ K. The value 6 here is nearly optimal.",
keywords = "(q1, q2)-quasimetric space, Box-quasimetric, Cartan group, Rashevskii–Chow theorem, horizontal broken line",
author = "Greshnov, {A. V.} and Kostyrkin, {V. S.}",
note = "Сведения о финансировании: Ministry of Education and Science of the Russian Federation 075-15-2022-282 ",
year = "2024",
month = dec,
day = "21",
doi = "10.1007/s10469-024-09767-w",
language = "English",
volume = "1",
pages = "10--20",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "63",

}

RIS

TY - JOUR

T1 - Box-Quasimetrics and Horizontal Joinability on Cartan Groups

AU - Greshnov, A. V.

AU - Kostyrkin, V. S.

N1 - Сведения о финансировании: Ministry of Education and Science of the Russian Federation 075-15-2022-282

PY - 2024/12/21

Y1 - 2024/12/21

N2 - On a Cartan group K equipped with a Carnot–Carathéodory metric dcc, we find the exact value of a constant in the (1, q2)-generalized triangle inequality for its Box-quasimetric. It is proved that any two points x, y ∈ K can be joined by a horizontal k-broken line Lx,yk, k ≤ 6; moreover, the length of such a broken line Lx,yk does not exceed the quantity Cdcc(x, y) for some constant C not depending on the choice of x, y ∈ K. The value 6 here is nearly optimal.

AB - On a Cartan group K equipped with a Carnot–Carathéodory metric dcc, we find the exact value of a constant in the (1, q2)-generalized triangle inequality for its Box-quasimetric. It is proved that any two points x, y ∈ K can be joined by a horizontal k-broken line Lx,yk, k ≤ 6; moreover, the length of such a broken line Lx,yk does not exceed the quantity Cdcc(x, y) for some constant C not depending on the choice of x, y ∈ K. The value 6 here is nearly optimal.

KW - (q1, q2)-quasimetric space

KW - Box-quasimetric

KW - Cartan group

KW - Rashevskii–Chow theorem

KW - horizontal broken line

UR - https://www.mendeley.com/catalogue/2ac846cb-0bb7-3b11-830c-ac1db9dc72c8/

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85212861167&origin=inward

U2 - 10.1007/s10469-024-09767-w

DO - 10.1007/s10469-024-09767-w

M3 - Article

VL - 1

SP - 10

EP - 20

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 63

ER -

ID: 61413226