Diameter and Laplace eigenvalue estimates for left-invariant metrics on compact Lie groups

DOI10.1007/s11118-021-09932-1OpenAlexW3172130615WikidataQ115381379 ScholiaQ115381379MaRDI QIDQ2681943

Emilio A. Lauret

Publication date: 31 January 2023

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.00350

zbMATH Keywords

diametereigenvalue estimateLaplaceleft-invariant metrichomogeneous metric

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Compact groups (22C05) Spectral theory; eigenvalue problems on manifolds (58C40) Sub-Riemannian geometry (53C17)

Related Items

Lipschitz Carnot-Carathéodory structures and their limits ⋮ Diameter and Laplace eigenvalue estimates for compact homogeneous Riemannian manifolds

Uses Software

• MathOverflow

Cites Work

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• Cut locus of a left invariant Riemannian metric on \(\mathrm{SO}_3\) in the axisymmetric case
• Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres
• Injectivity radius and Cartan polyhedron for simply connected symmetric spaces
• Injectivity radius for non-simply connected symmetric spaces via Cartan polyhedron
• On the least positive eigenvalue of Laplacian for compact homogeneous spaces
• Eigenvalue estimates on homogeneous manifolds
• On the diameter of compact homogeneous Riemannian manifolds
• Eigenvalue comparison theorems and its geometric applications
• On the least positive eigenvalue of the Laplacian for compact group manifolds
• Non-closed Lie subgroups of Lie groups
• Diameters of homogeneous spaces
• Lower bound estimates of the first eigenvalue for compact manifolds with positive Ricci curvature
• Diameter of the Berger sphere
• Left-invariant geometries on \(\operatorname{SU}(2)\) are uniformly doubling
• Upper bounds for the spectral function on homogeneous spaces via volume growth
• A rigidity theorem for subalgebras of Lie and associative algebras
• Hypoelliptic second order differential equations
• A Panoramic View of Riemannian Geometry
• The smallest Laplace eigenvalue of homogeneous 3-spheres
• A Comprehensive Introduction to Sub-Riemannian Geometry
• Spectral Geometry of the Laplacian
• On the smallest Laplace eigenvalue for naturally reductive metrics on compact simple Lie groups
• On Everywhere Dense Imbedding of Free Groups in Lie Groups
• Lie groups beyond an introduction