Exponential Growth and the Spectrum of the Laplacian

DOI10.2307/2043964zbMath0466.58028OpenAlexW4243237786MaRDI QIDQ3918787

Robert Brooks

Publication date: 1981

Full work available at URL: https://doi.org/10.2307/2043964

zbMATH Keywords

sub-exponential growthheat kernel for the heat equationsectional curvatures bounded from belowsmooth complete non-compact Riemannian manifoldspectrum of the Laplacian acting on functionsvolume of geodesic ball

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

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A relation between growth and the spectrum of the Laplacian ⋮ Eigenvalue estimates for the weighted Laplacian on a Riemannian manifold ⋮ A note on constant mean curvature foliations of noncompact Riemannian manifolds ⋮ Curvature estimate for the volume growth of globally minimal submanifolds ⋮ On the entropies of hypersurfaces with bounded mean curvature

Cites Work

• The fundamental group and the spectrum of the Laplacian
• Asymptotic expansions for the compact quotients of properly discontinuous group actions
• A note on curvature and fundamental group
• An upper bound to the spectrum of \(\Delta\) on a manifold of negative curvature
• A lower bound for the heat kernel
• Differential equations on riemannian manifolds and their geometric applications
• Isoperimetric constants and the first eigenvalue of a compact riemannian manifold
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