Left-invariant geometries on \(\operatorname{SU}(2)\) are uniformly doubling

DOI10.1007/s00039-018-0457-8zbMath1407.53034arXiv1708.03021OpenAlexW3098725885MaRDI QIDQ1794367

Maria Gordina, Laurent Saloff-Coste, Nathaniel Eldredge

Publication date: 15 October 2018

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.03021

zbMATH Keywords

Poincaré inequalityheat kernelcompact Lie groupspecial unitary groupsub-Riemannian manifoldvolume doubling

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Differential geometry of homogeneous manifolds (53C30) Analysis on real and complex Lie groups (22E30) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Compact groups (22C05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Sub-Riemannian geometry (53C17) Manifolds of metrics (especially Riemannian) (58D17) Heat kernel (35K08)

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Diameter and Laplace eigenvalue estimates for left-invariant metrics on compact Lie groups, Heat kernel estimates on Harnack manifolds and beyond, On the smallest Laplace eigenvalue for naturally reductive metrics on compact simple Lie groups, Diameter and Laplace eigenvalue estimates for compact homogeneous Riemannian manifolds, The first eigenvalue of a homogeneous CROSS

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