Weighted \(p\)-harmonic functions and rigidity of smooth metric measure spaces

DOI10.1016/j.jmaa.2016.05.065zbMath1342.53064OpenAlexW2419286235MaRDI QIDQ302047

Nguyen Duy Dat, Nguyen Thac Dung

Publication date: 4 July 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.05.065

zbMATH Keywords

Harnack inequalityLiouville propertygradient estimatessmooth metric measure spacesweighted \(p\)-harmonic functions

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items

Vanishing properties of $p$-harmonic $\ell$-forms on Riemannian manifolds ⋮ Gradient estimates for weighted \(p\)-Laplacian equations on Riemannian manifolds with a Sobolev inequality and integral Ricci bounds ⋮ Positive solutions of the \(p\)-Laplacian with potential terms on weighted Riemannian manifolds with linear diameter growth ⋮ A quantitative second order estimate for (weighted) \(p\)-harmonic functions in manifolds under curvature-dimension condition ⋮ LIOUVILLE PROPERTY FOR <i>f</i>-HARMONIC FUNCTIONS WITH POLYNOMIAL GROWTH ⋮ \(p\)-harmonic \(\ell\)-forms on Riemannian manifolds with a weighted Poincaré inequality

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A splitting theorem for the weighted measure
• Local gradient estimate for \(p\)-harmonic functions on Riemannian manifolds
• Smooth metric measure spaces with non-negative curvature
• Analysis of weighted Laplacian and applications to Ricci solitons
• Sharp gradient estimate and spectral rigidity for \(p\)-Laplacian
• Ends of metric measure spaces and Sobolev inequalities
• The inverse mean curvature flow and \(p\)-harmonic functions
• Li-Yau type estimates for a nonlinear parabolic equation on complete manifolds
• On the parabolic kernel of the Schrödinger operator
• Regularity for a more general class of quasilinear equations
• Complete manifolds with positive spectrum
• Complete manifolds with positive spectrum. II.
• A note on the splitting theorem for the weighted measure
• A Liouville-type theorem for smooth metric measure spaces
• Eigenvalue estimate for the weighted \(p\)-Laplacian
• Gradient estimates and entropy formulae for weighted \(p\)-heat equations on smooth metric measure spaces
• \(L^p\)-Liouville theorems on complete smooth metric measure spaces
• Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds
• Weighted Poincaré inequality and rigidity of complete manifolds
• Local gradient estimates of $p$-harmonic functions, $1/H$-flow, and an entropy formula
• Connectedness at infinity of complete Kähler manifolds
• On the Liouville Theorem for Harmonic Maps
• A note on the isoperimetric constant
• Differential equations on riemannian manifolds and their geometric applications