Estimates for eigenvalues of the bi-drifting Laplacian operator

DOI10.1007/s00033-014-0426-5zbMath1333.58012OpenAlexW1980872638MaRDI QIDQ2355500

Feng Du, Chang-Yu Xia, Guang Han Li, Chuan Xi Wu

Publication date: 23 July 2015

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-014-0426-5

zbMATH Keywords

eigenvaluesdrifting Laplacianuniversal inequalitiesGaussian shrinking soliton

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global Riemannian geometry, including pinching (53C20)

Related Items (20)

Eigenvalue inequalities for the buckling problem of the drifting Laplacian on Ricci solitons ⋮ Universal inequalities for eigenvalues of a system of elliptic equations of the drifting Laplacian ⋮ Universal inequalities of the poly-drifting Laplacian on smooth metric measure spaces ⋮ Universal inequalities on complete noncompact smooth metric measure spaces ⋮ Eigenvalue inequalities for the buckling problem of the drifting Laplacian ⋮ Universal inequalities for eigenvalues of a clamped plate problem of the drifting Laplacian ⋮ Estimates for the eigenvalues of the bi-drifting Laplacian on complete metric measure spaces ⋮ Eigenvalues of Witten-Laplacian on the cigar metric measure spaces ⋮ Universal inequalities of the poly-drifting Laplacian on the Gaussian and cylinder shrinking solitons ⋮ Estimates for eigenvalues of a system of elliptic equations with drift and of bi-drifting Laplacian ⋮ Eigenvalue inequalities for the Markov diffusion operator ⋮ Eigenvalue inequalities of elliptic operators in weighted divergence form on smooth metric measure spaces ⋮ Sharp lower bounds for the first eigenvalues of the bi-drifting Laplacian ⋮ Estimates for eigenvalues of weighted Laplacian and weighted \(p\)-Laplacian ⋮ Eigenvalue inequalities for the buckling problem of the drifting Laplacian of arbitrary order ⋮ Unnamed Item ⋮ Estimates for the eigenvalues of the bi-drifting Laplacian on cigar soliton ⋮ Eigenvalues of the bi-drifting Laplacian on the complete noncompact Riemannian manifolds ⋮ Inequalities for eigenvalues of fourth-order elliptic operators in divergence form on complete Riemannian manifolds ⋮ Universal bounds for eigenvalues of the polydrifting Laplacian operator in compact domains in the \(\mathbb R^n\) and \(\mathbb S^n\)

Cites Work

• Unnamed Item
• Generic mean curvature flow. I: Generic singularities
• Extension of Reilly formula with applications to eigenvalue estimates for drifting Laplacians
• Inequalities for eigenvalues of elliptic operators in divergence form on Riemannian manifolds
• Inequalities for eigenvalues of the biharmonic operator
• Universal bounds for eigenvalues of a buckling problem
• Universal bounds for eigenvalues of the biharmonic operator on Riemannian manifolds
• Convexity of the first eigenfunction of the drifting Laplacian operator and its applications
• Estimates for lower order eigenvalues of a clamped plate problem
• Convex eigenfunction of a drifting Laplacian operator and the fundamental gap
• Geometry of horospheres
• Eigenvalue estimates on homogeneous manifolds
• On Riemannian manifolds admitting a function whose gradient is of constant norm
• Inequalities for eigenvalues of the drifting Laplacian on Riemannian manifolds
• On the Ratio of Consecutive Eigenvalues
• Recent Progress on Ricci Solitons
• Universal inequalities for the eigenvalues of Laplace and Schrödinger operators on submanifolds
• Inequalities for eigenvalues of a clamped plate problem

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