(q 1, q 2)-quasimetrics bi-Lipschitz equivalent to 1-quasimetrics Full article
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Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126 |
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| Output data | Year: 2017, Volume: 27, Number: 4, Pages: 253-262 Pages count : 10 DOI: 10.3103/S1055134417040034 | ||||
| Tags | (q1, q2)-quasimetric; Carnot–Carathéodory space; chain approximation; distance function; extreme point; generalized triangle inequality | ||||
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Abstract:
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.
Cite:
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
Original:
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
Identifiers:
| Scopus: | 2-s2.0-85036551701 |
| OpenAlex: | W2770948235 |