Abstract
Let M be a connected compact smooth Riemannian manifold, and let ∆ = − div(grad) its Laplacian operator of L 2(M). Its eigenvalues λ0 = 0 < λl(M) ≤ λ2(M) ≤ ··· form a discrete subset (with multiplicities) of ℝ+.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Basel AG
About this chapter
Cite this chapter
Lubotzky, A. (1994). The Laplacian and its Eigenvalues. In: Discrete Groups, Expanding Graphs and Invariant Measures. Modern Birkhäuser Classics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0346-0332-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-0346-0332-4_4
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0346-0331-7
Online ISBN: 978-3-0346-0332-4
eBook Packages: Springer Book Archive