Exact values of constants in the generalized triangle inequality for some \((1, q_2)\)-quasimetrics on canonical Carnot groups

DOI10.1134/S0001434615090369zbMath1348.22010MaRDI QIDQ276696

M. V. Tryamkin, Aleksandr Valer'evich Greshnov

Publication date: 4 May 2016

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

Heisenberg groupBaker-Campbell-Hausdorff formulabox quasimetriccanonical Carnot groupCarnot algebraEngel groupgeneralized triangle inequality

Mathematics Subject Classification ID

Graded Lie (super)algebras (17B70) General properties and structure of real Lie groups (22E15)

Related Items (11)

Horizontal joinability in canonical 3-step Carnot groups with corank 2 horizontal distributions ⋮ $ (q_1,q_2)$-quasimetric spaces. Covering mappings and coincidence points ⋮ Regularization of distance functions and separation axioms on \((q_1,q_2)\)-quasimetric spaces ⋮ Ekeland variational principle in complete weakly symmetric (1, q₂)-quasimetric spaces and applications ⋮ The Agrachev-Barilari-Boscain method and estimates for the number of segments of horizontal broken lines joining points in the canonical Carnot group \(G_{3,3}\) ⋮ (q1,q2)-quasimetric spaces. Covering mappings and coincidence points. A review of the results ⋮ Horizontal joinability on 5-dimensional 2-step Carnot groups with a codimension 2 horizontal distribution ⋮ (q1, q2)-quasimetrics bi-Lipschitz equivalent to 1-quasimetrics ⋮ On finding the exact values of the constant in a \((1,q_2)\)-generalized triangle inequality for box-quasimetrics on 2-step Carnot groups with 1-dimensional center ⋮ Optimal horizontal joinability on the Engel group ⋮ Hyperspaces that satisfy \(cc\)-homogeneous cone condition on canonical Heisenberg and Engel groups

Cites Work

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• On the Hausdorff volume in sub-Riemannian geometry
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• Hypoelliptic differential operators and nilpotent groups
• Geometry of Carnot-Carathéodory Spaces, Differentiability, Coarea and Area Formulas
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians

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