About coincidence points theorems on 2-step Carnot groups with 1-dimensional centre equipped with Box-quasimetrics

Alexander Greshnov; Vladimir Potapov; Alexander Greshnov; Vladimir Potapov

doi:10.3934/math.2023313

AIMS Mathematics

2023, Volume 8, Issue 3: 6191-6205. doi: 10.3934/math.2023313

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About coincidence points theorems on 2-step Carnot groups with 1-dimensional centre equipped with Box-quasimetrics

Alexander Greshnov ^,,
Vladimir Potapov

Sobolev Institute of Mathematics, Koptyuga ave., Novosibirsk 630090, Russia

Received: 30 October 2022 Revised: 21 December 2022 Accepted: 25 December 2022 Published: 03 January 2023
MSC : 54H25, 43A80

For some class of 2-step Carnot groups $ D_n $ with 1-dimensional centre we find the exact values of the constants in $ (1, q_2) $-generalized triangle inequality for their $ \text{Box} $-quasimetrics $ \rho_{\text{Box}_{D_n}} $. Using this result we get the best version of the Coincidence Points Theorem of $ \alpha $-covering and $ \beta $-Lipschitz mappings defined on $ (D_n, \rho_{\text{Box}_{D_n}}) $.
- $ (q_1, q_2) $-quasimetric spase,
- Carnot group,
- exact value,
- $\text{Box}$-quasimetric,
- coincidence points,
- estimates of divergence
Citation: Alexander Greshnov, Vladimir Potapov. About coincidence points theorems on 2-step Carnot groups with 1-dimensional centre equipped with Box-quasimetrics[J]. AIMS Mathematics, 2023, 8(3): 6191-6205. doi: 10.3934/math.2023313

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Abstract

For some class of 2-step Carnot groups $ D_n $ with 1-dimensional centre we find the exact values of the constants in $ (1, q_2) $-generalized triangle inequality for their $ \text{Box} $-quasimetrics $ \rho_{\text{Box}_{D_n}} $. Using this result we get the best version of the Coincidence Points Theorem of $ \alpha $-covering and $ \beta $-Lipschitz mappings defined on $ (D_n, \rho_{\text{Box}_{D_n}}) $.

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