(q 1, q 2)-quasimetrics bi-Lipschitz equivalent to 1-quasimetrics Научная публикация
| Журнал |
Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126 |
||||
|---|---|---|---|---|---|
| Вых. Данные | Год: 2017, Том: 27, Номер: 4, Страницы: 253-262 Страниц : 10 DOI: 10.3103/S1055134417040034 | ||||
| Ключевые слова | (q1, q2)-quasimetric; Carnot–Carathéodory space; chain approximation; distance function; extreme point; generalized triangle inequality | ||||
| Авторы |
|
||||
| Организации |
|
Реферат:
We prove that the conditions of (q1, 1)- and (1, q2)-quasimertricity of a distance function ρ are sufficient for the existence of a quasimetric bi-Lipschitz equivalent to ρ. It follows that the Box-quasimetric defined with the use of basis vector fields of class C1 whose commutators at most sum their degrees is bi-Lipschitz equivalent to some metric. On the other hand, we show that these conditions are not necessary. We prove the existence of (q1, q2)-quasimetrics for which there are no Lipschitz equivalent 1-quasimetrics, which in particular implies another proof of a result by V. Schröder. © 2017, Allerton Press, Inc.
Библиографическая ссылка:
Greshnov A.V.
(q 1, q 2)-quasimetrics bi-Lipschitz equivalent to 1-quasimetrics
Siberian Advances in Mathematics. 2017. V.27. N4. P.253-262. DOI: 10.3103/S1055134417040034 Scopus OpenAlex
(q 1, q 2)-quasimetrics bi-Lipschitz equivalent to 1-quasimetrics
Siberian Advances in Mathematics. 2017. V.27. N4. P.253-262. DOI: 10.3103/S1055134417040034 Scopus OpenAlex
Оригинальная:
Грешнов А.В.
(q1,q2)- Квазиметрики, билипшицево эквивалентные 1-квазиметрикам
Математические труды. 2017. Т.20. №1. С.81–96. DOI: 10.17377/mattrudy.2017.20.105
(q1,q2)- Квазиметрики, билипшицево эквивалентные 1-квазиметрикам
Математические труды. 2017. Т.20. №1. С.81–96. DOI: 10.17377/mattrudy.2017.20.105
Идентификаторы БД:
| Scopus: | 2-s2.0-85036551701 |
| OpenAlex: | W2770948235 |