Weighted Cheeger constant and first eigenvalue lower bound estimates on smooth metric measure spaces

DOI10.1186/s13662-021-03431-8zbMath1494.58012OpenAlexW3170493390MaRDI QIDQ2167011

Akram Ali, Abimbola Abolarinwa, Ali Alkhadi

Publication date: 25 August 2022

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-021-03431-8

zbMATH Keywords

eigenvaluesRiemannian manifoldmean curvatureCheeger constantdrifting Laplacian

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items

Variation of the first eigenvalue of Witten Laplacian and consequences under super Perelman-Ricci flow ⋮ The Cheeger problem in abstract measure spaces

Cites Work

• Smooth metric measure spaces with non-negative curvature
• Analysis of weighted Laplacian and applications to Ricci solitons
• Extension of Reilly formula with applications to eigenvalue estimates for drifting Laplacians
• On eigenvalues of a system of elliptic equations and of the biharmonic operator
• Comparison estimates on the first eigenvalue of a quasilinear elliptic system
• An extension of Barta's theorem and geometric applications
• The lower bounds of the first eigenvalues for the biharmonic operator on manifolds
• Eigenvalue estimates for the \(p\)-Laplace operator on manifolds
• Eigenvalue estimates for submanifolds with locally bounded mean curvature
• \(p\)-Fundamental tone estimates of submanifolds with bounded mean curvature
• Eigenvalue estimate for the weighted \(p\)-Laplacian
• First eigenvalue for the \(p\)-Laplace operator
• Monotonicity formulas for the first eigenvalue of the weighted \(p\)-Laplacian under the Ricci-harmonic flow
• On the spectrum of the weighted \(p\)-Laplacian under the Ricci-harmonic flow
• Eigenvalues of Witten-Laplacian on the cigar metric measure spaces
• On the spectrum of the \(p\)-biharmonic operator under the Ricci flow
• On the first eigenvalue of the Witten-Laplacian and the diameter of compact shrinking solitons
• An upper bound to the spectrum of \(\Delta\) on a manifold of negative curvature
• Isoperimetric constants and the first eigenvalue of a compact riemannian manifold
• Analysis and Geometry of Markov Diffusion Operators
• Geometric estimates on weighted p-fundamental tone and applications to the first eigenvalue of submanifolds with bounded mean curvature
• Estimates for the eigenvalues of the bi-drifting Laplacian on complete metric measure spaces
• Eigenvalue estimates for submanifolds with bounded mean curvature in the hyperbolic space
• Lower bound estimates for the first eigenvalue of the weighted \(p\)-Laplacian on smooth metric measure spaces
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