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

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}}) $.

Keywords

• (q₁，qsub>2</sub>)-quasimetric spase
• carnot group
• exact value
• box-quasimetric
• coincidence points
• estimates of divergence