The Horofunction boundary of the Heisenberg Group: The Carnot-Carathéodory metric

DOI10.1090/S1088-4173-2010-00217-1zbMath1218.22005MaRDI QIDQ2997810

Tom Klein, Andrew J. Nicas

Publication date: 9 May 2011

Published in: Conformal Geometry and Dynamics of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Heisenberg groupisometriesCarnot-Carathéodory metrichorofunction boundaryBusemann point

Mathematics Subject Classification ID

Geometric group theory (20F65) Nilpotent and solvable Lie groups (22E25) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Direct methods ((G)-spaces of Busemann, etc.) (53C70)

Related Items

Toric varieties vs. horofunction compactifications of polyhedral norms, Isometric embeddings into Heisenberg groups, Asymptotic behavior of the Riemannian Heisenberg group and its horoboundary, Unnamed Item, Sub-Finsler horofunction boundaries of the Heisenberg group

Cites Work

• The horofunction boundary of the Heisenberg group
• An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
• Geometric properties of Heisenberg-type groups
• Some regularity theorems for Carnot-Caratheodory metrics
• Group \(C^*\)-algebras as compact quantum metric spaces
• Geodesics and isometries of Carnot groups
• The horofunction boundary of finite-dimensional normed spaces
• Unnamed Item
• Unnamed Item