TY - JOUR

T1 - Box-Quasimetrics and Horizontal Joinability on Cartan Groups

AU - Greshnov, A. V.

AU - Kostyrkin, V. S.

N1 - Supported by Mathematical Center in Akademgorodok, Agreement with RF Ministry of Education and Science No. 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 - ГРУППА КАРТАНА

KW - (q1,q2)-КВАЗИМЕТРИЧЕСКОЕ ПРОСТРАНСТВО

KW - ВОХ-КВАЗИМЕТРИКА

KW - ГОРИЗОНТАЛЬНАЯ ЛОМАНАЯ

KW - ТЕОРЕМА РАШЕВСКОГО-ЧОУ

KW - (q1, q2)-quasimetric space

KW - Box-quasimetric

KW - Cartan group

KW - Rashevskii–Chow theorem

KW - horizontal broken line

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

UR - https://elibrary.ru/item.asp?id=80205222

UR - https://elibrary.ru/item.asp?id=80383473

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

U2 - 10.1007/s10469-024-09767-w

DO - 10.1007/s10469-024-09767-w

M3 - Article

VL - 63

SP - 10

EP - 20

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 1

M1 - 2

ER -