Geometry of balls in nilpotent Lie groups

DOI10.1215/S0012-7094-94-07415-2zbMath0810.53041OpenAlexW2014958512WikidataQ115240152 ScholiaQ115240152MaRDI QIDQ1331680

Ron Karidi

Publication date: 9 April 1995

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

Full work available at URL: https://doi.org/10.1215/s0012-7094-94-07415-2

zbMATH Keywords

nilpotent Lie groupinvariant Riemannian metric

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Nilpotent and solvable Lie groups (22E25)

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Some examples of quasiisometries of nilpotent Lie groups ⋮ On the Čech cohomology of Morse boundaries ⋮ Extremals in some classes of Carnot groups ⋮ On the Cheng-Yau gradient estimate for Carnot groups and sub-Riemannian manifolds ⋮ Some properties of abnormal extremals on Lie groups ⋮ A note on Carnot geodesics in nilpotent Lie groups ⋮ The asymptotic density of finite-order elements in virtually nilpotent groups. ⋮ Holomorphic functions of exponential type on connected complex Lie groups ⋮ Large scale geometry of nilpotent-by-cyclic groups ⋮ Geometric characterizations of embedding theorems: for Sobolev, Besov, and Triebel-Lizorkin spaces on spaces of homogeneous type -- via orthonormal wavelets ⋮ Arens–Michael envelopes of nilpotent Lie algebras, holomorphic functions of exponential type, and homological epimorphisms

Cites Work

• Models for free nilpotent Lie algebras
• Balls and metrics defined by vector fields. I: Basic properties
• Ricci structure and volume growth for left invariant Riemannian metrics on nilpotent and some solvable Lie groups
• A note on curvature and fundamental group
• Growth of finitely generated solvable groups and curvature of Riemannian manifolds
• Croissance polynomiale et périodes des fonctions harmoniques
• Unnamed Item