Lower bound estimates for the first eigenvalue of the weighted \(p\)-Laplacian on smooth metric measure spaces

DOI10.1016/j.difgeo.2015.11.008zbMath1334.58020arXiv1512.01031OpenAlexW2964159053WikidataQ115355783 ScholiaQ115355783MaRDI QIDQ5964087

Yu-Zhao Wang, Huai-Qian Li

Publication date: 26 February 2016

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.01031

zbMATH Keywords

eigenvalue estimateweighted \(p\)-LaplacianBakry-Émery Ricci curvaturesmooth metric measure spaceweighted \(p\)-Bochner formulaweighted \(p\)-Reilly formula

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Elliptic equations on manifolds, general theory (58J05) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (25)

Gradient estimates for weighted \(p\)-Laplacian equations on Riemannian manifolds with a Sobolev inequality and integral Ricci bounds ⋮ Weighted Cheeger constant and first eigenvalue lower bound estimates on smooth metric measure spaces ⋮ First eigenvalue of the \(p\)-Laplacian under integral curvature condition ⋮ Gradient estimates for \(p\)-Laplacian Lichnerowicz equation on noncompact metric measure space ⋮ Unnamed Item ⋮ Rigidity properties of smooth metric measure spaces via the weighted 𝑝-Laplacian ⋮ Logarithmic Harnack inequalities and gradient estimates for nonlinear \(p\)-Laplace equations on weighted Riemannian manifolds ⋮ Upper bounds on the first eigenvalue for the \(p\)-Laplacian ⋮ Gradient estimates for positive weak solution to \(\Delta_p u + au^\sigma = 0\) on Riemannian manifolds ⋮ Lower bounds for the length of the second fundamental form via the first eigenvalue of the \(p\)-Laplacian ⋮ Liouville type theorems for nonlinear \(p\)-Laplacian equation on complete noncompact Riemannian manifolds ⋮ Logarithmic Harnack inequalities and differential Harnack estimates for \(p\)-Laplacian on Riemannian manifolds ⋮ First eigenvalue of the $p$-Laplacian on Kähler manifolds ⋮ Gradient estimates and Liouville type theorems for \((p-1)^{p-1}\Delta_pu+au^{p-1}\log u^{p-1}=0\) on Riemannian manifolds ⋮ Comparison geometry for an extension of Ricci tensor ⋮ Eigenvalue estimates of the \(p\)-Laplacian on finite graphs ⋮ Boundary effect of \(m\)-dimensional Bakry-Émery Ricci curvature ⋮ Gradient estimates for the 𝑝-Laplacian Lichnerowicz equation on smooth metric measure spaces ⋮ On the eigenvalue problem involving the weighted \(p\)-Laplacian in radially symmetric domains ⋮ Sharp lower bound for the first eigenvalue of the weighted \(p\)-Laplacian. I ⋮ 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 ⋮ Symmetry for positive critical points of Caffarelli-Kohn-Nirenberg inequalities ⋮ The overdetermined problem and lower bound estimate on the first nonzero Steklov eigenvalue of \(p\)-Laplacian ⋮ Evolution of the first eigenvalue of weighted \(p\)-Laplacian along the Ricci-Bourguignon flow

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